exp_30_runs_two_attr – Complete Experiment Report

two_attr_corr

▼

Vary_Correlation_with_high_Dimension (MvNormal, correlation, 30 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -7.575 3.47e-10 -1.843
HMC 0.3 2.309 0.0258 0.940
HMC 0.5 4.277 0.000146 2.778
HMC 0.9 6.108 7.09e-07 4.421
HMC 0.99 6.064 1.14e-06 7.808
SMC 0.0 -0.395 0.694 -0.101
SMC 0.3 -0.054 0.958 -0.012
SMC 0.5 1.462 0.149 0.404
SMC 0.9 -0.024 0.981 -0.006
SMC 0.99 1.160 0.251 0.326
Metro 0.0 14.074 6.54e-19 4.761
Metro 0.3 6.690 2.03e-07 8.959
Metro 0.5 5.331 9.52e-06 9.594
Metro 0.9 7.114 7.6e-08 21.662
Metro 0.99 7.518 2.74e-08 65.387
DEMetro_Z 0.0 41.477 2.25e-27 2215.116
DEMetro_Z 0.3 40.550 4.28e-27 1128.335
DEMetro_Z 0.5 39.997 6.32e-27 878.867
DEMetro_Z 0.9 41.384 2.36e-27 510.899
DEMetro_Z 0.99 41.240 2.6e-27 465.804
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -41.545 2.15e-27 -7.585
HMC_vs_DEMetro_Z 0.3 -40.514 4.41e-27 -7.397
HMC_vs_DEMetro_Z 0.5 -40.089 5.96e-27 -7.319
HMC_vs_DEMetro_Z 0.9 -41.591 2.09e-27 -7.593
HMC_vs_DEMetro_Z 0.99 -41.046 3.04e-27 -7.494
Metro_vs_SMC 0.0 13.370 6.27e-14 2.441
Metro_vs_SMC 0.3 6.884 1.46e-07 1.257
Metro_vs_SMC 0.5 4.975 2.72e-05 0.908
Metro_vs_SMC 0.9 7.177 6.71e-08 1.310
Metro_vs_SMC 0.99 7.449 3.29e-08 1.360
Metro_vs_DEMetro_Z 0.0 -41.366 2.44e-27 -7.552
Metro_vs_DEMetro_Z 0.3 -40.989 3.16e-27 -7.483
Metro_vs_DEMetro_Z 0.5 -39.241 1.1e-26 -7.164
Metro_vs_DEMetro_Z 0.9 -38.624 1.72e-26 -7.052
Metro_vs_DEMetro_Z 0.99 -28.206 1.24e-22 -5.150
HMC_vs_Metro 0.0 -19.778 2.22e-18 -3.611
HMC_vs_Metro 0.3 -5.533 5.77e-06 -1.010
HMC_vs_Metro 0.5 -3.614 0.00113 -0.660
HMC_vs_Metro 0.9 -5.533 5.78e-06 -1.010
HMC_vs_Metro 0.99 -6.416 5.13e-07 -1.171
HMC_vs_SMC 0.0 -9.093 5.46e-10 -1.660
HMC_vs_SMC 0.3 2.281 0.0301 0.416
HMC_vs_SMC 0.5 4.070 0.000331 0.743
HMC_vs_SMC 0.9 6.059 1.36e-06 1.106
HMC_vs_SMC 0.99 6.038 1.44e-06 1.102
DEMetro_Z_vs_SMC 0.0 41.451 2.3e-27 7.568
DEMetro_Z_vs_SMC 0.3 40.516 4.41e-27 7.397
DEMetro_Z_vs_SMC 0.5 40.104 5.9e-27 7.322
DEMetro_Z_vs_SMC 0.9 41.406 2.37e-27 7.560
DEMetro_Z_vs_SMC 0.99 41.183 2.76e-27 7.519
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.018 0.023 0.003 -1.843
HMC 0.3 0.028 0.023 0.006 0.940
HMC 0.5 0.042 0.021 0.008 2.778
HMC 0.9 0.079 0.019 0.013 4.421
HMC 0.99 0.119 0.019 0.013 7.808
SMC 0.0 0.023 0.023 0.003 -0.101
SMC 0.3 0.023 0.023 0.006 -0.012
SMC 0.5 0.024 0.021 0.008 0.404
SMC 0.9 0.019 0.019 0.013 -0.006
SMC 0.99 0.023 0.019 0.013 0.326
Metro 0.0 0.037 0.023 0.003 4.761
Metro 0.3 0.076 0.023 0.006 8.959
Metro 0.5 0.094 0.021 0.008 9.594
Metro 0.9 0.310 0.019 0.013 21.662
Metro 0.99 0.858 0.019 0.013 65.387
DEMetro_Z 0.0 6.543 0.023 0.003 2215.116
DEMetro_Z 0.3 6.762 0.023 0.006 1128.335
DEMetro_Z 0.5 6.672 0.021 0.008 878.867
DEMetro_Z 0.9 6.870 0.019 0.013 510.899
DEMetro_Z 0.99 5.991 0.019 0.013 465.804
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 8.416 5.25e-11 2.951
HMC 0.3 5.135 3.76e-06 1.496
HMC 0.5 2.801 0.00826 1.686
HMC 0.9 4.935 2.85e-05 7.665
HMC 0.99 5.353 8.31e-06 6.476
SMC 0.0 3.182 0.00245 0.997
SMC 0.3 1.999 0.0512 0.680
SMC 0.5 2.734 0.00868 0.935
SMC 0.9 2.246 0.0301 0.955
SMC 0.99 -1.420 0.161 -0.388
Metro 0.0 14.662 2.18e-18 5.870
Metro 0.3 10.248 1.29e-11 8.570
Metro 0.5 7.823 1.06e-08 13.085
Metro 0.9 6.405 5.19e-07 27.776
Metro 0.99 5.108 1.88e-05 117.039
DEMetro_Z 0.0 31.296 6.68e-24 46855.551
DEMetro_Z 0.3 35.735 1.57e-25 42367.030
DEMetro_Z 0.5 43.085 7.62e-28 34672.650
DEMetro_Z 0.9 40.696 3.88e-27 19905.158
DEMetro_Z 0.99 35.603 1.74e-25 8465.852
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 6.923 1.31e-07 1.264
HMC_vs_SMC 0.3 2.222 0.0342 0.406
HMC_vs_SMC 0.5 1.176 0.249 0.215
HMC_vs_SMC 0.9 4.054 0.000346 0.740
HMC_vs_SMC 0.99 5.567 5.25e-06 1.016
Metro_vs_DEMetro_Z 0.0 -31.293 6.7e-24 -5.713
Metro_vs_DEMetro_Z 0.3 -35.739 1.56e-25 -6.525
Metro_vs_DEMetro_Z 0.5 -43.057 7.76e-28 -7.861
Metro_vs_DEMetro_Z 0.9 -40.622 4.09e-27 -7.416
Metro_vs_DEMetro_Z 0.99 -34.621 3.85e-25 -6.321
HMC_vs_Metro 0.0 -7.905 1.02e-08 -1.443
HMC_vs_Metro 0.3 -7.957 8.93e-09 -1.453
HMC_vs_Metro 0.5 -6.999 1.07e-07 -1.278
HMC_vs_Metro 0.9 -4.369 0.000146 -0.798
HMC_vs_Metro 0.99 -4.824 4.13e-05 -0.881
HMC_vs_DEMetro_Z 0.0 -31.294 6.69e-24 -5.714
HMC_vs_DEMetro_Z 0.3 -35.735 1.57e-25 -6.524
HMC_vs_DEMetro_Z 0.5 -43.078 7.65e-28 -7.865
HMC_vs_DEMetro_Z 0.9 -40.685 3.91e-27 -7.428
HMC_vs_DEMetro_Z 0.99 -35.575 1.78e-25 -6.495
Metro_vs_SMC 0.0 12.158 6.59e-13 2.220
Metro_vs_SMC 0.3 9.767 1.12e-10 1.783
Metro_vs_SMC 0.5 7.104 8.13e-08 1.297
Metro_vs_SMC 0.9 5.916 2.01e-06 1.080
Metro_vs_SMC 0.99 5.118 1.83e-05 0.934
DEMetro_Z_vs_SMC 0.0 31.295 6.69e-24 5.714
DEMetro_Z_vs_SMC 0.3 35.737 1.56e-25 6.525
DEMetro_Z_vs_SMC 0.5 43.083 7.63e-28 7.866
DEMetro_Z_vs_SMC 0.9 40.692 3.89e-27 7.429
DEMetro_Z_vs_SMC 0.99 35.609 1.73e-25 6.501
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.042 0.032 0.004 2.951
HMC 0.3 0.037 0.031 0.004 1.496
HMC 0.5 0.039 0.030 0.005 1.686
HMC 0.9 0.095 0.024 0.009 7.665
HMC 0.99 0.154 0.034 0.018 6.476
SMC 0.0 0.035 0.032 0.004 0.997
SMC 0.3 0.034 0.031 0.004 0.680
SMC 0.5 0.035 0.030 0.005 0.935
SMC 0.9 0.033 0.024 0.009 0.955
SMC 0.99 0.027 0.034 0.018 -0.388
Metro 0.0 0.052 0.032 0.004 5.870
Metro 0.3 0.068 0.031 0.004 8.570
Metro 0.5 0.099 0.030 0.005 13.085
Metro 0.9 0.282 0.024 0.009 27.776
Metro 0.99 2.198 0.034 0.018 117.039
DEMetro_Z 0.0 166.178 0.032 0.004 46855.551
DEMetro_Z 0.3 183.099 0.031 0.004 42367.030
DEMetro_Z 0.5 181.841 0.030 0.005 34672.650
DEMetro_Z 0.9 184.755 0.024 0.009 19905.158
DEMetro_Z 0.99 156.561 0.034 0.018 8465.852
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -2.475 0.0163 -0.604
HMC 0.3 3.416 0.00144 1.461
HMC 0.5 4.469 9.19e-05 3.624
HMC 0.9 7.218 4.11e-08 7.320
HMC 0.99 9.176 3.24e-10 12.746
SMC 0.0 0.139 0.89 0.036
SMC 0.3 0.188 0.851 0.041
SMC 0.5 1.812 0.0754 0.514
SMC 0.9 0.627 0.533 0.159
SMC 0.99 1.402 0.166 0.374
Metro 0.0 15.833 5.86e-20 6.055
Metro 0.3 7.773 1.19e-08 12.413
Metro 0.5 5.989 1.57e-06 14.394
Metro 0.9 9.800 9.89e-11 35.751
Metro 0.99 11.973 9.49e-13 120.398
DEMetro_Z 0.0 61.863 2.37e-32 5860.936
DEMetro_Z 0.3 69.837 7.18e-34 3153.652
DEMetro_Z 0.5 92.846 1.92e-37 2450.664
DEMetro_Z 0.9 96.813 5.65e-38 1461.432
DEMetro_Z 0.99 68.671 1.15e-33 1199.616
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -61.721 2.53e-32 -11.269
Metro_vs_DEMetro_Z 0.3 -69.683 7.67e-34 -12.722
Metro_vs_DEMetro_Z 0.5 -88.338 8.14e-37 -16.128
Metro_vs_DEMetro_Z 0.9 -89.771 5.12e-37 -16.390
Metro_vs_DEMetro_Z 0.99 -56.031 4.09e-31 -10.230
DEMetro_Z_vs_SMC 0.0 61.832 2.4e-32 11.289
DEMetro_Z_vs_SMC 0.3 69.861 7.13e-34 12.755
DEMetro_Z_vs_SMC 0.5 93.032 1.82e-37 16.985
DEMetro_Z_vs_SMC 0.9 96.886 5.64e-38 17.689
DEMetro_Z_vs_SMC 0.99 68.604 1.2e-33 12.525
HMC_vs_DEMetro_Z 0.0 -61.880 2.35e-32 -11.298
HMC_vs_DEMetro_Z 0.3 -69.850 7.16e-34 -12.753
HMC_vs_DEMetro_Z 0.5 -93.028 1.83e-37 -16.985
HMC_vs_DEMetro_Z 0.9 -96.357 6.61e-38 -17.592
HMC_vs_DEMetro_Z 0.99 -69.192 9.4e-34 -12.633
HMC_vs_Metro 0.0 -17.042 1.2e-16 -3.111
HMC_vs_Metro 0.3 -6.391 5.48e-07 -1.167
HMC_vs_Metro 0.5 -4.277 0.000188 -0.781
HMC_vs_Metro 0.9 -7.503 2.86e-08 -1.370
HMC_vs_Metro 0.99 -10.193 4.27e-11 -1.861
HMC_vs_SMC 0.0 -3.178 0.00351 -0.580
HMC_vs_SMC 0.3 3.272 0.00276 0.597
HMC_vs_SMC 0.5 4.239 0.000209 0.774
HMC_vs_SMC 0.9 6.886 1.45e-07 1.257
HMC_vs_SMC 0.99 9.354 2.94e-10 1.708
Metro_vs_SMC 0.0 13.958 2.12e-14 2.548
Metro_vs_SMC 0.3 7.854 1.16e-08 1.434
Metro_vs_SMC 0.5 5.655 4.12e-06 1.033
Metro_vs_SMC 0.9 9.836 9.59e-11 1.796
Metro_vs_SMC 0.99 11.875 1.17e-12 2.168
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.028 0.029 0.002 -0.604
HMC 0.3 0.034 0.029 0.003 1.461
HMC 0.5 0.043 0.027 0.004 3.624
HMC 0.9 0.079 0.024 0.007 7.320
HMC 0.99 0.127 0.024 0.008 12.746
SMC 0.0 0.029 0.029 0.002 0.036
SMC 0.3 0.029 0.029 0.003 0.041
SMC 0.5 0.029 0.027 0.004 0.514
SMC 0.9 0.025 0.024 0.007 0.159
SMC 0.99 0.027 0.024 0.008 0.374
Metro 0.0 0.040 0.029 0.002 6.055
Metro 0.3 0.070 0.029 0.003 12.413
Metro 0.5 0.089 0.027 0.004 14.394
Metro 0.9 0.290 0.024 0.007 35.751
Metro 0.99 0.994 0.024 0.008 120.398
DEMetro_Z 0.0 10.069 0.029 0.002 5860.936
DEMetro_Z 0.3 10.515 0.029 0.003 3153.652
DEMetro_Z 0.5 10.599 0.027 0.004 2450.664
DEMetro_Z 0.9 10.870 0.024 0.007 1461.432
DEMetro_Z 0.99 9.683 0.024 0.008 1199.616
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -3.952 0.000234 -0.884
HMC 0.3 3.081 0.00363 1.277
HMC 0.5 4.484 8.52e-05 3.364
HMC 0.9 6.884 1.09e-07 7.602
HMC 0.99 8.385 2.24e-09 10.996
SMC 0.0 0.914 0.365 0.219
SMC 0.3 0.965 0.339 0.222
SMC 0.5 2.236 0.0293 0.622
SMC 0.9 1.177 0.244 0.342
SMC 0.99 0.587 0.559 0.155
Metro 0.0 14.499 7.44e-20 4.640
Metro 0.3 8.609 1.31e-09 11.767
Metro 0.5 6.843 1.52e-07 15.474
Metro 0.9 9.538 1.82e-10 35.948
Metro 0.99 15.669 1.03e-15 80.319
DEMetro_Z 0.0 97.693 2.92e-38 326.961
DEMetro_Z 0.3 85.705 1.04e-36 227.241
DEMetro_Z 0.5 93.201 6.43e-38 201.167
DEMetro_Z 0.9 90.416 2.51e-38 115.739
DEMetro_Z 0.99 97.440 2.66e-40 93.676
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 99.156 2.89e-38 18.103
DEMetro_Z_vs_SMC 0.3 85.209 2.31e-36 15.557
DEMetro_Z_vs_SMC 0.5 93.198 1.73e-37 17.016
DEMetro_Z_vs_SMC 0.9 91.710 2.76e-37 16.744
DEMetro_Z_vs_SMC 0.99 95.164 9.48e-38 17.374
HMC_vs_Metro 0.0 -18.516 1.31e-17 -3.381
HMC_vs_Metro 0.3 -7.011 1.04e-07 -1.280
HMC_vs_Metro 0.5 -5.144 1.7e-05 -0.939
HMC_vs_Metro 0.9 -7.146 7.27e-08 -1.305
HMC_vs_Metro 0.99 -13.011 1.24e-13 -2.375
Metro_vs_DEMetro_Z 0.0 -96.141 7.05e-38 -17.553
Metro_vs_DEMetro_Z 0.3 -78.932 2.1e-35 -14.411
Metro_vs_DEMetro_Z 0.5 -58.911 9.67e-32 -10.756
Metro_vs_DEMetro_Z 0.9 -21.550 2.15e-19 -3.935
Metro_vs_DEMetro_Z 0.99 -2.621 0.0138 -0.478
HMC_vs_SMC 0.0 -6.617 2.98e-07 -1.208
HMC_vs_SMC 0.3 2.574 0.0154 0.470
HMC_vs_SMC 0.5 4.181 0.000245 0.763
HMC_vs_SMC 0.9 6.462 4.52e-07 1.180
HMC_vs_SMC 0.99 8.385 3.05e-09 1.531
Metro_vs_SMC 0.0 13.369 6.28e-14 2.441
Metro_vs_SMC 0.3 8.492 2.34e-09 1.550
Metro_vs_SMC 0.5 6.416 5.12e-07 1.171
Metro_vs_SMC 0.9 9.423 2.5e-10 1.720
Metro_vs_SMC 0.99 15.640 1.14e-15 2.855
HMC_vs_DEMetro_Z 0.0 -99.031 3e-38 -18.080
HMC_vs_DEMetro_Z 0.3 -84.604 2.84e-36 -15.447
HMC_vs_DEMetro_Z 0.5 -91.946 2.56e-37 -16.787
HMC_vs_DEMetro_Z 0.9 -66.179 3.39e-33 -12.083
HMC_vs_DEMetro_Z 0.99 -58.270 1.32e-31 -10.639
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.013 0.014 0.002 -0.884
HMC 0.3 0.018 0.015 0.002 1.277
HMC 0.5 0.024 0.014 0.003 3.364
HMC 0.9 0.050 0.014 0.005 7.602
HMC 0.99 0.079 0.015 0.006 10.996
SMC 0.0 0.015 0.014 0.002 0.219
SMC 0.3 0.015 0.015 0.002 0.222
SMC 0.5 0.016 0.014 0.003 0.622
SMC 0.9 0.015 0.014 0.005 0.342
SMC 0.99 0.016 0.015 0.006 0.155
Metro 0.0 0.022 0.014 0.002 4.640
Metro 0.3 0.044 0.015 0.002 11.767
Metro 0.5 0.057 0.014 0.003 15.474
Metro 0.9 0.185 0.014 0.005 35.948
Metro 0.99 0.485 0.015 0.006 80.319
DEMetro_Z 0.0 0.570 0.014 0.002 326.961
DEMetro_Z 0.3 0.578 0.015 0.002 227.241
DEMetro_Z 0.5 0.575 0.014 0.003 201.167
DEMetro_Z 0.9 0.566 0.014 0.005 115.739
DEMetro_Z 0.99 0.564 0.015 0.006 93.676
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -7.841 1.82e-10 -1.790
HMC 0.3 1.702 0.0959 0.682
HMC 0.5 3.656 0.000862 2.418
HMC 0.9 4.841 3.32e-05 4.585
HMC 0.99 4.552 8.52e-05 9.191
SMC 0.0 -0.459 0.648 -0.124
SMC 0.3 0.947 0.348 0.270
SMC 0.5 0.513 0.61 0.132
SMC 0.9 -0.424 0.673 -0.096
SMC 0.99 0.458 0.649 0.138
Metro 0.0 15.213 1.33e-20 4.945
Metro 0.3 6.912 9.84e-08 7.330
Metro 0.5 6.585 2.93e-07 11.766
Metro 0.9 7.971 8.48e-09 43.089
Metro 0.99 6.634 2.84e-07 109.335
DEMetro_Z 0.0 21.905 1.37e-19 3704.994
DEMetro_Z 0.3 45.126 2.03e-28 1972.704
DEMetro_Z 0.5 35.886 1.39e-25 1563.810
DEMetro_Z 0.9 43.628 5.29e-28 900.256
DEMetro_Z 0.99 31.470 5.69e-24 764.866
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -21.914 1.36e-19 -4.001
HMC_vs_DEMetro_Z 0.3 -45.247 1.88e-28 -8.261
HMC_vs_DEMetro_Z 0.5 -35.738 1.56e-25 -6.525
HMC_vs_DEMetro_Z 0.9 -43.710 5.05e-28 -7.980
HMC_vs_DEMetro_Z 0.99 -31.586 5.15e-24 -5.767
Metro_vs_SMC 0.0 16.637 2.26e-16 3.037
Metro_vs_SMC 0.3 6.330 6.48e-07 1.156
Metro_vs_SMC 0.5 6.724 2.23e-07 1.228
Metro_vs_SMC 0.9 7.996 8.09e-09 1.460
Metro_vs_SMC 0.99 6.589 3.21e-07 1.203
Metro_vs_DEMetro_Z 0.0 -21.882 1.42e-19 -3.995
Metro_vs_DEMetro_Z 0.3 -44.829 2.45e-28 -8.185
Metro_vs_DEMetro_Z 0.5 -35.967 1.3e-25 -6.567
Metro_vs_DEMetro_Z 0.9 -44.248 3.56e-28 -8.079
Metro_vs_DEMetro_Z 0.99 -23.154 3e-20 -4.227
HMC_vs_Metro 0.0 -22.948 3.83e-20 -4.190
HMC_vs_Metro 0.3 -5.710 3.54e-06 -1.043
HMC_vs_Metro 0.5 -4.640 6.89e-05 -0.847
HMC_vs_Metro 0.9 -7.069 8.92e-08 -1.291
HMC_vs_Metro 0.99 -6.330 6.47e-07 -1.156
HMC_vs_SMC 0.0 -8.069 6.74e-09 -1.473
HMC_vs_SMC 0.3 1.055 0.3 0.193
HMC_vs_SMC 0.5 3.418 0.00189 0.624
HMC_vs_SMC 0.9 5.100 1.92e-05 0.931
HMC_vs_SMC 0.99 4.279 0.000187 0.781
DEMetro_Z_vs_SMC 0.0 21.913 1.36e-19 4.001
DEMetro_Z_vs_SMC 0.3 45.173 1.97e-28 8.247
DEMetro_Z_vs_SMC 0.5 35.849 1.43e-25 6.545
DEMetro_Z_vs_SMC 0.9 43.621 5.35e-28 7.964
DEMetro_Z_vs_SMC 0.99 31.390 6.14e-24 5.731
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.018 0.023 0.003 -1.790
HMC 0.3 0.027 0.023 0.006 0.682
HMC 0.5 0.039 0.021 0.008 2.418
HMC 0.9 0.081 0.019 0.013 4.585
HMC 0.99 0.137 0.019 0.013 9.191
SMC 0.0 0.023 0.023 0.003 -0.124
SMC 0.3 0.024 0.023 0.006 0.270
SMC 0.5 0.022 0.021 0.008 0.132
SMC 0.9 0.018 0.019 0.013 -0.096
SMC 0.99 0.021 0.019 0.013 0.138
Metro 0.0 0.038 0.023 0.003 4.945
Metro 0.3 0.066 0.023 0.006 7.330
Metro 0.5 0.110 0.021 0.008 11.766
Metro 0.9 0.597 0.019 0.013 43.089
Metro 0.99 1.421 0.019 0.013 109.335
DEMetro_Z 0.0 10.928 0.023 0.003 3704.994
DEMetro_Z 0.3 11.805 0.023 0.006 1972.704
DEMetro_Z 0.5 11.855 0.021 0.008 1563.810
DEMetro_Z 0.9 12.091 0.019 0.013 900.256
DEMetro_Z 0.99 9.825 0.019 0.013 764.866
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 9.591 5.51e-13 3.139
HMC 0.3 4.906 1.11e-05 1.719
HMC 0.5 3.691 0.000637 1.538
HMC 0.9 3.640 0.00104 9.526
HMC 0.99 5.735 2.72e-06 6.295
SMC 0.0 -0.381 0.705 -0.110
SMC 0.3 1.336 0.187 0.403
SMC 0.5 1.099 0.276 0.323
SMC 0.9 0.888 0.379 0.329
SMC 0.99 -1.903 0.0621 -0.537
Metro 0.0 13.549 1.84e-16 6.193
Metro 0.3 11.987 8.29e-14 7.563
Metro 0.5 7.720 1.33e-08 11.358
Metro 0.9 7.021 1e-07 38.864
Metro 0.99 38.591 1.68e-27 43.333
DEMetro_Z 0.0 16.216 4.42e-16 6154.027
DEMetro_Z 0.3 15.300 2.01e-15 4299.505
DEMetro_Z 0.5 15.921 7.15e-16 4034.718
DEMetro_Z 0.9 13.642 3.78e-14 2424.092
DEMetro_Z 0.99 13.071 1.11e-13 1241.396
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 10.128 4.95e-11 1.849
HMC_vs_SMC 0.3 3.948 0.000461 0.721
HMC_vs_SMC 0.5 2.513 0.0178 0.459
HMC_vs_SMC 0.9 3.502 0.00151 0.639
HMC_vs_SMC 0.99 6.145 1.07e-06 1.122
Metro_vs_DEMetro_Z 0.0 -16.201 4.53e-16 -2.958
Metro_vs_DEMetro_Z 0.3 -15.279 2.09e-15 -2.790
Metro_vs_DEMetro_Z 0.5 -15.867 7.82e-16 -2.897
Metro_vs_DEMetro_Z 0.9 -13.435 5.55e-14 -2.453
Metro_vs_DEMetro_Z 0.99 -12.610 2.69e-13 -2.302
HMC_vs_Metro 0.0 -6.458 4.57e-07 -1.179
HMC_vs_Metro 0.3 -9.258 3.68e-10 -1.690
HMC_vs_Metro 0.5 -7.081 8.65e-08 -1.293
HMC_vs_Metro 0.9 -4.518 9.65e-05 -0.825
HMC_vs_Metro 0.99 -22.291 8.51e-20 -4.070
HMC_vs_DEMetro_Z 0.0 -16.205 4.5e-16 -2.959
HMC_vs_DEMetro_Z 0.3 -15.296 2.03e-15 -2.793
HMC_vs_DEMetro_Z 0.5 -15.915 7.23e-16 -2.906
HMC_vs_DEMetro_Z 0.9 -13.572 4.3e-14 -2.478
HMC_vs_DEMetro_Z 0.99 -12.998 1.27e-13 -2.373
Metro_vs_SMC 0.0 12.516 3.24e-13 2.285
Metro_vs_SMC 0.3 11.006 7.18e-12 2.009
Metro_vs_SMC 0.5 7.471 3.11e-08 1.364
Metro_vs_SMC 0.9 6.873 1.5e-07 1.255
Metro_vs_SMC 0.99 37.459 4.11e-26 6.839
DEMetro_Z_vs_SMC 0.0 16.218 4.41e-16 2.961
DEMetro_Z_vs_SMC 0.3 15.299 2.02e-15 2.793
DEMetro_Z_vs_SMC 0.5 15.921 7.15e-16 2.907
DEMetro_Z_vs_SMC 0.9 13.637 3.82e-14 2.490
DEMetro_Z_vs_SMC 0.99 13.074 1.1e-13 2.387
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.043 0.032 0.004 3.139
HMC 0.3 0.038 0.031 0.004 1.719
HMC 0.5 0.038 0.030 0.005 1.538
HMC 0.9 0.112 0.024 0.009 9.526
HMC 0.99 0.151 0.034 0.018 6.295
SMC 0.0 0.031 0.032 0.004 -0.110
SMC 0.3 0.033 0.031 0.004 0.403
SMC 0.5 0.032 0.030 0.005 0.323
SMC 0.9 0.027 0.024 0.009 0.329
SMC 0.99 0.025 0.034 0.018 -0.537
Metro 0.0 0.054 0.032 0.004 6.193
Metro 0.3 0.064 0.031 0.004 7.563
Metro 0.5 0.089 0.030 0.005 11.358
Metro 0.9 0.384 0.024 0.009 38.864
Metro 0.99 0.836 0.034 0.018 43.333
DEMetro_Z 0.0 21.853 0.032 0.004 6154.027
DEMetro_Z 0.3 18.609 0.031 0.004 4299.505
DEMetro_Z 0.5 21.187 0.030 0.005 4034.718
DEMetro_Z 0.9 22.521 0.024 0.009 2424.092
DEMetro_Z 0.99 22.987 0.034 0.018 1241.396
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -2.321 0.0241 -0.533
HMC 0.3 2.716 0.00964 1.176
HMC 0.5 4.099 0.000259 3.117
HMC 0.9 7.090 6.53e-08 8.620
HMC 0.99 5.528 5.67e-06 14.520
SMC 0.0 -0.890 0.377 -0.231
SMC 0.3 0.827 0.412 0.245
SMC 0.5 0.598 0.552 0.157
SMC 0.9 0.082 0.935 0.019
SMC 0.99 0.413 0.682 0.123
Metro 0.0 16.688 7.05e-21 6.350
Metro 0.3 7.298 3.97e-08 10.200
Metro 0.5 7.456 2.97e-08 16.492
Metro 0.9 8.472 2.44e-09 64.005
Metro 0.99 7.582 2.33e-08 150.042
DEMetro_Z 0.0 23.129 3.09e-20 5285.783
DEMetro_Z 0.3 48.657 2.34e-29 2926.699
DEMetro_Z 0.5 39.077 1.23e-26 2294.562
DEMetro_Z 0.9 41.280 2.58e-27 1351.611
DEMetro_Z 0.99 31.765 4.38e-24 1028.680
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -23.108 3.16e-20 -4.219
Metro_vs_DEMetro_Z 0.3 -48.483 2.6e-29 -8.852
Metro_vs_DEMetro_Z 0.5 -39.095 1.22e-26 -7.138
Metro_vs_DEMetro_Z 0.9 -42.093 1.48e-27 -7.685
Metro_vs_DEMetro_Z 0.99 -23.869 1.29e-20 -4.358
DEMetro_Z_vs_SMC 0.0 23.134 3.07e-20 4.224
DEMetro_Z_vs_SMC 0.3 48.681 2.31e-29 8.888
DEMetro_Z_vs_SMC 0.5 39.033 1.27e-26 7.126
DEMetro_Z_vs_SMC 0.9 41.293 2.56e-27 7.539
DEMetro_Z_vs_SMC 0.99 31.700 4.65e-24 5.788
HMC_vs_DEMetro_Z 0.0 -23.130 3.08e-20 -4.223
HMC_vs_DEMetro_Z 0.3 -48.733 2.24e-29 -8.897
HMC_vs_DEMetro_Z 0.5 -38.918 1.39e-26 -7.105
HMC_vs_DEMetro_Z 0.9 -41.108 2.91e-27 -7.505
HMC_vs_DEMetro_Z 0.99 -31.819 4.19e-24 -5.809
HMC_vs_Metro 0.0 -18.257 1.91e-17 -3.333
HMC_vs_Metro 0.3 -6.058 1.36e-06 -1.106
HMC_vs_Metro 0.5 -5.353 9.52e-06 -0.977
HMC_vs_Metro 0.9 -7.140 7.39e-08 -1.304
HMC_vs_Metro 0.99 -7.191 6.45e-08 -1.313
HMC_vs_SMC 0.0 -1.559 0.13 -0.285
HMC_vs_SMC 0.3 2.231 0.0336 0.407
HMC_vs_SMC 0.5 3.916 0.000502 0.715
HMC_vs_SMC 0.9 7.143 7.33e-08 1.304
HMC_vs_SMC 0.99 5.308 1.08e-05 0.969
Metro_vs_SMC 0.0 18.154 2.22e-17 3.315
Metro_vs_SMC 0.3 6.882 1.46e-07 1.256
Metro_vs_SMC 0.5 7.539 2.61e-08 1.376
Metro_vs_SMC 0.9 8.489 2.36e-09 1.550
Metro_vs_SMC 0.99 7.540 2.6e-08 1.377
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.028 0.029 0.002 -0.533
HMC 0.3 0.033 0.029 0.003 1.176
HMC 0.5 0.041 0.027 0.004 3.117
HMC 0.9 0.088 0.024 0.007 8.620
HMC 0.99 0.141 0.024 0.008 14.520
SMC 0.0 0.029 0.029 0.002 -0.231
SMC 0.3 0.030 0.029 0.003 0.245
SMC 0.5 0.028 0.027 0.004 0.157
SMC 0.9 0.024 0.024 0.007 0.019
SMC 0.99 0.025 0.024 0.008 0.123
Metro 0.0 0.040 0.029 0.002 6.350
Metro 0.3 0.063 0.029 0.003 10.200
Metro 0.5 0.098 0.027 0.004 16.492
Metro 0.9 0.499 0.024 0.007 64.005
Metro 0.99 1.233 0.024 0.008 150.042
DEMetro_Z 0.0 9.084 0.029 0.002 5285.783
DEMetro_Z 0.3 9.760 0.029 0.003 2926.699
DEMetro_Z 0.5 9.926 0.027 0.004 2294.562
DEMetro_Z 0.9 10.055 0.024 0.007 1351.611
DEMetro_Z 0.99 8.307 0.024 0.008 1028.680
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -2.962 0.00454 -0.676
HMC 0.3 2.593 0.0131 1.104
HMC 0.5 4.303 0.000143 3.174
HMC 0.9 7.602 1.67e-08 9.413
HMC 0.99 5.961 1.67e-06 12.614
SMC 0.0 -0.513 0.61 -0.129
SMC 0.3 1.203 0.234 0.354
SMC 0.5 1.228 0.224 0.337
SMC 0.9 0.449 0.655 0.121
SMC 0.99 0.219 0.827 0.061
Metro 0.0 14.544 1.2e-19 4.815
Metro 0.3 8.393 2e-09 9.593
Metro 0.5 8.172 4.62e-09 16.899
Metro 0.9 9.611 1.58e-10 59.796
Metro 0.99 13.425 5.58e-14 121.968
DEMetro_Z 0.0 64.268 7.48e-33 545.423
DEMetro_Z 0.3 80.072 1.14e-35 373.254
DEMetro_Z 0.5 55.709 4.38e-31 339.407
DEMetro_Z 0.9 105.939 1.04e-39 197.012
DEMetro_Z 0.99 108.870 1.6e-40 153.380
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 64.156 8.3e-33 11.713
DEMetro_Z_vs_SMC 0.3 79.322 1.83e-35 14.482
DEMetro_Z_vs_SMC 0.5 55.109 6.58e-31 10.061
DEMetro_Z_vs_SMC 0.9 104.313 6.66e-39 19.045
DEMetro_Z_vs_SMC 0.99 106.552 3.61e-39 19.454
HMC_vs_Metro 0.0 -18.349 1.67e-17 -3.350
HMC_vs_Metro 0.3 -7.012 1.04e-07 -1.280
HMC_vs_Metro 0.5 -5.891 2.15e-06 -1.076
HMC_vs_Metro 0.9 -7.837 1.21e-08 -1.431
HMC_vs_Metro 0.99 -12.566 2.94e-13 -2.294
Metro_vs_DEMetro_Z 0.0 -63.625 1.05e-32 -11.616
Metro_vs_DEMetro_Z 0.3 -77.729 3.28e-35 -14.191
Metro_vs_DEMetro_Z 0.5 -53.525 1.52e-30 -9.772
Metro_vs_DEMetro_Z 0.9 -21.429 2.51e-19 -3.912
Metro_vs_DEMetro_Z 0.99 -3.445 0.00176 -0.629
HMC_vs_SMC 0.0 -3.101 0.00427 -0.566
HMC_vs_SMC 0.3 1.908 0.0663 0.348
HMC_vs_SMC 0.5 3.839 0.000619 0.701
HMC_vs_SMC 0.9 7.551 2.53e-08 1.379
HMC_vs_SMC 0.99 5.737 3.28e-06 1.047
Metro_vs_SMC 0.0 17.410 6.79e-17 3.179
Metro_vs_SMC 0.3 7.883 1.08e-08 1.439
Metro_vs_SMC 0.5 8.232 4.46e-09 1.503
Metro_vs_SMC 0.9 9.667 1.41e-10 1.765
Metro_vs_SMC 0.99 13.318 6.92e-14 2.431
HMC_vs_DEMetro_Z 0.0 -64.276 7.86e-33 -11.735
HMC_vs_DEMetro_Z 0.3 -80.315 1.27e-35 -14.663
HMC_vs_DEMetro_Z 0.5 -53.745 1.35e-30 -9.812
HMC_vs_DEMetro_Z 0.9 -90.062 4.66e-37 -16.443
HMC_vs_DEMetro_Z 0.99 -57.620 1.83e-31 -10.520
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.013 0.014 0.002 -0.676
HMC 0.3 0.017 0.015 0.002 1.104
HMC 0.5 0.023 0.014 0.003 3.174
HMC 0.9 0.058 0.014 0.005 9.413
HMC 0.99 0.089 0.015 0.006 12.614
SMC 0.0 0.014 0.014 0.002 -0.129
SMC 0.3 0.015 0.015 0.002 0.354
SMC 0.5 0.015 0.014 0.003 0.337
SMC 0.9 0.014 0.014 0.005 0.121
SMC 0.99 0.015 0.015 0.006 0.061
Metro 0.0 0.023 0.014 0.002 4.815
Metro 0.3 0.038 0.015 0.002 9.593
Metro 0.5 0.061 0.014 0.003 16.899
Metro 0.9 0.299 0.014 0.005 59.796
Metro 0.99 0.729 0.015 0.006 121.968
DEMetro_Z 0.0 0.941 0.014 0.002 545.423
DEMetro_Z 0.3 0.940 0.015 0.002 373.254
DEMetro_Z 0.5 0.960 0.014 0.003 339.407
DEMetro_Z 0.9 0.953 0.014 0.005 197.012
DEMetro_Z 0.99 0.914 0.015 0.006 153.380
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Trace Plots
Pooled
0.0 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.9 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.99 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
0.0 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.9 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.99 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
0.0
0.3
0.5
0.9
0.99
Chain
0.0
0.3
0.5
0.9
0.99

Vary_Correlation_with_heavy_Tails (MvStudentT, correlation, 30 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -0.460 0.647 -0.113
HMC 0.3 1.800 0.0771 0.499
HMC 0.5 -0.014 0.989 -0.004
HMC 0.9 2.553 0.0143 1.037
HMC 0.99 2.829 0.00744 1.416
SMC 0.0 3.443 0.00108 0.948
SMC 0.3 3.260 0.00208 1.180
SMC 0.5 2.422 0.0192 0.827
SMC 0.9 2.978 0.00497 1.406
SMC 0.99 3.853 0.000384 1.554
Metro 0.0 3.686 0.000567 1.250
Metro 0.3 4.251 0.000112 1.715
Metro 0.5 2.720 0.0103 1.843
Metro 0.9 4.809 3.66e-05 4.571
Metro 0.99 3.769 0.000746 41.472
DEMetro_Z 0.0 4.488 4.13e-05 1.460
DEMetro_Z 0.3 4.630 3.64e-05 1.996
DEMetro_Z 0.5 3.035 0.00374 0.951
DEMetro_Z 0.9 3.112 0.00404 4.161
DEMetro_Z 0.99 3.856 0.00054 3.678
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -5.180 1.54e-05 -0.946
HMC_vs_DEMetro_Z 0.3 -4.161 0.000258 -0.760
HMC_vs_DEMetro_Z 0.5 -3.067 0.00465 -0.560
HMC_vs_DEMetro_Z 0.9 -2.362 0.0251 -0.431
HMC_vs_DEMetro_Z 0.99 -2.552 0.0162 -0.466
Metro_vs_SMC 0.0 0.805 0.427 0.147
Metro_vs_SMC 0.3 1.181 0.247 0.216
Metro_vs_SMC 0.5 1.332 0.193 0.243
Metro_vs_SMC 0.9 3.035 0.00504 0.554
Metro_vs_SMC 0.99 3.612 0.00113 0.659
Metro_vs_DEMetro_Z 0.0 -0.551 0.586 -0.101
Metro_vs_DEMetro_Z 0.3 -0.494 0.625 -0.090
Metro_vs_DEMetro_Z 0.5 1.282 0.21 0.234
Metro_vs_DEMetro_Z 0.9 0.236 0.815 0.043
Metro_vs_DEMetro_Z 0.99 3.386 0.00205 0.618
HMC_vs_Metro 0.0 -3.852 0.000597 -0.703
HMC_vs_Metro 0.3 -2.746 0.0103 -0.501
HMC_vs_Metro 0.5 -2.728 0.0107 -0.498
HMC_vs_Metro 0.9 -3.848 0.000604 -0.702
HMC_vs_Metro 0.99 -3.643 0.00104 -0.665
HMC_vs_SMC 0.0 -4.363 0.000148 -0.797
HMC_vs_SMC 0.3 -1.951 0.0607 -0.356
HMC_vs_SMC 0.5 -2.638 0.0133 -0.482
HMC_vs_SMC 0.9 -0.651 0.52 -0.119
HMC_vs_SMC 0.99 -0.212 0.833 -0.039
DEMetro_Z_vs_SMC 0.0 1.569 0.127 0.286
DEMetro_Z_vs_SMC 0.3 2.202 0.0357 0.402
DEMetro_Z_vs_SMC 0.5 0.316 0.754 0.058
DEMetro_Z_vs_SMC 0.9 2.015 0.0532 0.368
DEMetro_Z_vs_SMC 0.99 2.303 0.0287 0.420
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.060 0.065 0.042 -0.113
HMC 0.3 0.076 0.056 0.040 0.499
HMC 0.5 0.068 0.068 0.046 -0.004
HMC 0.9 0.075 0.047 0.027 1.037
HMC 0.99 0.105 0.052 0.037 1.416
SMC 0.0 0.105 0.065 0.042 0.948
SMC 0.3 0.103 0.056 0.040 1.180
SMC 0.5 0.107 0.068 0.046 0.827
SMC 0.9 0.084 0.047 0.027 1.406
SMC 0.99 0.110 0.052 0.037 1.554
Metro 0.0 0.117 0.065 0.042 1.250
Metro 0.3 0.124 0.056 0.040 1.715
Metro 0.5 0.154 0.068 0.046 1.843
Metro 0.9 0.169 0.047 0.027 4.571
Metro 0.99 1.603 0.052 0.037 41.472
DEMetro_Z 0.0 0.126 0.065 0.042 1.460
DEMetro_Z 0.3 0.135 0.056 0.040 1.996
DEMetro_Z 0.5 0.112 0.068 0.046 0.951
DEMetro_Z 0.9 0.158 0.047 0.027 4.161
DEMetro_Z 0.99 0.190 0.052 0.037 3.678
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 0.139 0.89 0.040
HMC 0.3 -0.122 0.903 -0.034
HMC 0.5 0.451 0.654 0.113
HMC 0.9 -0.858 0.395 -0.189
HMC 0.99 -0.400 0.691 -0.110
SMC 0.0 2.022 0.0489 0.431
SMC 0.3 4.721 1.59e-05 1.334
SMC 0.5 0.970 0.336 0.225
SMC 0.9 1.767 0.0829 0.410
SMC 0.99 4.495 3.64e-05 1.042
Metro 0.0 -1.614 0.116 -0.308
Metro 0.3 0.540 0.591 0.169
Metro 0.5 0.658 0.513 0.169
Metro 0.9 -0.069 0.946 -0.015
Metro 0.99 1.637 0.112 6.648
DEMetro_Z 0.0 -0.869 0.39 -0.177
DEMetro_Z 0.3 0.597 0.553 0.185
DEMetro_Z 0.5 0.490 0.626 0.124
DEMetro_Z 0.9 0.996 0.328 2.698
DEMetro_Z 0.99 -0.037 0.97 -0.009
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 -1.581 0.125 -0.289
HMC_vs_SMC 0.3 -5.161 1.62e-05 -0.942
HMC_vs_SMC 0.5 -1.541 0.134 -0.281
HMC_vs_SMC 0.9 -3.627 0.00109 -0.662
HMC_vs_SMC 0.99 -4.439 0.00012 -0.810
Metro_vs_DEMetro_Z 0.0 -1.518 0.14 -0.277
Metro_vs_DEMetro_Z 0.3 -0.146 0.885 -0.027
Metro_vs_DEMetro_Z 0.5 0.646 0.524 0.118
Metro_vs_DEMetro_Z 0.9 -1.002 0.325 -0.183
Metro_vs_DEMetro_Z 0.99 1.637 0.113 0.299
HMC_vs_Metro 0.0 1.565 0.128 0.286
HMC_vs_Metro 0.3 -1.137 0.265 -0.208
HMC_vs_Metro 0.5 -0.703 0.488 -0.128
HMC_vs_Metro 0.9 -2.925 0.00663 -0.534
HMC_vs_Metro 0.99 -1.657 0.108 -0.302
HMC_vs_DEMetro_Z 0.0 1.116 0.274 0.204
HMC_vs_DEMetro_Z 0.3 -1.324 0.196 -0.242
HMC_vs_DEMetro_Z 0.5 -0.300 0.766 -0.055
HMC_vs_DEMetro_Z 0.9 -1.063 0.296 -0.194
HMC_vs_DEMetro_Z 0.99 -0.681 0.501 -0.124
Metro_vs_SMC 0.0 -5.287 1.14e-05 -0.965
Metro_vs_SMC 0.3 -4.100 0.000304 -0.749
Metro_vs_SMC 0.5 -0.528 0.602 -0.096
Metro_vs_SMC 0.9 -2.341 0.0263 -0.427
Metro_vs_SMC 0.99 1.379 0.178 0.252
DEMetro_Z_vs_SMC 0.0 -4.039 0.00036 -0.737
DEMetro_Z_vs_SMC 0.3 -4.187 0.00024 -0.765
DEMetro_Z_vs_SMC 0.5 -1.449 0.158 -0.264
DEMetro_Z_vs_SMC 0.9 0.846 0.405 0.154
DEMetro_Z_vs_SMC 0.99 -4.578 8.19e-05 -0.836
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 9.675 9.112 14.240 0.040
HMC 0.3 4.529 4.697 4.977 -0.034
HMC 0.5 12.531 9.883 23.480 0.113
HMC 0.9 3.885 5.328 7.624 -0.189
HMC 0.99 5.186 6.084 8.146 -0.110
SMC 0.0 15.246 9.112 14.240 0.431
SMC 0.3 11.335 4.697 4.977 1.334
SMC 0.5 15.168 9.883 23.480 0.225
SMC 0.9 8.457 5.328 7.624 0.410
SMC 0.99 14.572 6.084 8.146 1.042
Metro 0.0 4.724 9.112 14.240 -0.308
Metro 0.3 5.539 4.697 4.977 0.169
Metro 0.5 13.862 9.883 23.480 0.169
Metro 0.9 5.214 5.328 7.624 -0.015
Metro 0.99 60.235 6.084 8.146 6.648
DEMetro_Z 0.0 6.585 9.112 14.240 -0.177
DEMetro_Z 0.3 5.615 4.697 4.977 0.185
DEMetro_Z 0.5 12.789 9.883 23.480 0.124
DEMetro_Z 0.9 25.895 5.328 7.624 2.698
DEMetro_Z 0.99 6.007 6.084 8.146 -0.009
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 2.276 0.03 2.414
HMC 0.3 3.056 0.00395 1.339
HMC 0.5 3.555 0.00093 1.425
HMC 0.9 6.244 6.53e-08 1.848
HMC 0.99 5.171 1.16e-05 3.960
SMC 0.0 12.599 1.96e-13 21.836
SMC 0.3 10.437 2.08e-11 21.953
SMC 0.5 9.130 3.94e-10 14.722
SMC 0.9 9.039 4.87e-10 14.312
SMC 0.99 17.277 6e-17 37.041
Metro 0.0 7.932 4.44e-10 3.026
Metro 0.3 7.852 1.54e-09 3.714
Metro 0.5 4.807 3.51e-05 4.046
Metro 0.9 8.979 1.8e-10 5.912
Metro 0.99 4.367 0.000146 69.076
DEMetro_Z 0.0 5.707 2.71e-06 5.219
DEMetro_Z 0.3 9.567 2.17e-11 5.390
DEMetro_Z 0.5 11.244 2.89e-15 3.771
DEMetro_Z 0.9 2.250 0.0321 7.228
DEMetro_Z 0.99 5.638 3.89e-06 8.245
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -2.259 0.0316 -0.412
Metro_vs_DEMetro_Z 0.3 -2.201 0.0358 -0.402
Metro_vs_DEMetro_Z 0.5 0.322 0.75 0.059
Metro_vs_DEMetro_Z 0.9 -0.387 0.701 -0.071
Metro_vs_DEMetro_Z 0.99 3.759 0.000767 0.686
DEMetro_Z_vs_SMC 0.0 -8.873 9.26e-10 -1.620
DEMetro_Z_vs_SMC 0.3 -7.465 3.16e-08 -1.363
DEMetro_Z_vs_SMC 0.5 -7.182 6.62e-08 -1.311
DEMetro_Z_vs_SMC 0.9 -1.930 0.0635 -0.352
DEMetro_Z_vs_SMC 0.99 -10.904 8.94e-12 -1.991
HMC_vs_DEMetro_Z 0.0 -2.262 0.0314 -0.413
HMC_vs_DEMetro_Z 0.3 -7.964 8.78e-09 -1.454
HMC_vs_DEMetro_Z 0.5 -6.488 4.21e-07 -1.185
HMC_vs_DEMetro_Z 0.9 -1.645 0.111 -0.300
HMC_vs_DEMetro_Z 0.99 -2.848 0.008 -0.520
HMC_vs_Metro 0.0 -0.589 0.56 -0.108
HMC_vs_Metro 0.3 -3.881 0.000552 -0.709
HMC_vs_Metro 0.5 -2.860 0.00777 -0.522
HMC_vs_Metro 0.9 -7.097 8.27e-08 -1.296
HMC_vs_Metro 0.99 -4.118 0.00029 -0.752
HMC_vs_SMC 0.0 -9.270 3.58e-10 -1.692
HMC_vs_SMC 0.3 -9.671 1.4e-10 -1.766
HMC_vs_SMC 0.5 -8.292 3.85e-09 -1.514
HMC_vs_SMC 0.9 -8.050 7.07e-09 -1.470
HMC_vs_SMC 0.99 -13.836 2.65e-14 -2.526
Metro_vs_SMC 0.0 -10.753 1.24e-11 -1.963
Metro_vs_SMC 0.3 -8.696 1.42e-09 -1.588
Metro_vs_SMC 0.5 -5.392 8.53e-06 -0.985
Metro_vs_SMC 0.9 -4.810 4.3e-05 -0.878
Metro_vs_SMC 0.99 2.031 0.0515 0.371
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.208 0.124 0.035 2.414
HMC 0.3 0.153 0.116 0.027 1.339
HMC 0.5 0.171 0.120 0.036 1.425
HMC 0.9 0.177 0.115 0.034 1.848
HMC 0.99 0.205 0.109 0.024 3.960
SMC 0.0 0.887 0.124 0.035 21.836
SMC 0.3 0.711 0.116 0.027 21.953
SMC 0.5 0.654 0.120 0.036 14.722
SMC 0.9 0.596 0.115 0.034 14.312
SMC 0.99 1.011 0.109 0.024 37.041
Metro 0.0 0.230 0.124 0.035 3.026
Metro 0.3 0.217 0.116 0.027 3.714
Metro 0.5 0.267 0.120 0.036 4.046
Metro 0.9 0.313 0.115 0.034 5.912
Metro 0.99 1.791 0.109 0.024 69.076
DEMetro_Z 0.0 0.306 0.124 0.035 5.219
DEMetro_Z 0.3 0.262 0.116 0.027 5.390
DEMetro_Z 0.5 0.257 0.120 0.036 3.771
DEMetro_Z 0.9 0.358 0.115 0.034 7.228
DEMetro_Z 0.99 0.310 0.109 0.024 8.245
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 2.044 0.0496 2.200
HMC 0.3 3.385 0.00143 1.193
HMC 0.5 2.288 0.0289 1.901
HMC 0.9 6.524 6.45e-08 2.650
HMC 0.99 3.990 0.000358 3.196
SMC 0.0 15.334 1.39e-15 31.158
SMC 0.3 13.095 8.6e-14 30.008
SMC 0.5 12.521 2.6e-13 27.485
SMC 0.9 12.904 1.11e-13 23.405
SMC 0.99 24.304 4.37e-21 45.812
Metro 0.0 8.760 1.55e-10 4.599
Metro 0.3 7.717 4.61e-09 4.562
Metro 0.5 11.258 1.68e-13 5.871
Metro 0.9 9.483 1.1e-10 9.336
Metro 0.99 10.744 1.22e-11 52.976
DEMetro_Z 0.0 7.587 1.27e-08 6.476
DEMetro_Z 0.3 10.497 5.25e-12 7.800
DEMetro_Z 0.5 9.643 3.4e-11 6.531
DEMetro_Z 0.9 5.826 2.11e-06 6.439
DEMetro_Z 0.99 8.033 5.28e-09 9.704
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 -12.092 7.52e-13 -2.208
DEMetro_Z_vs_SMC 0.3 -8.856 9.64e-10 -1.617
DEMetro_Z_vs_SMC 0.5 -9.928 7.77e-11 -1.813
DEMetro_Z_vs_SMC 0.9 -7.450 3.28e-08 -1.360
DEMetro_Z_vs_SMC 0.99 -16.326 3.7e-16 -2.981
HMC_vs_Metro 0.0 -1.954 0.0604 -0.357
HMC_vs_Metro 0.3 -5.388 8.62e-06 -0.984
HMC_vs_Metro 0.5 -4.061 0.000339 -0.741
HMC_vs_Metro 0.9 -6.514 3.93e-07 -1.189
HMC_vs_Metro 0.99 -10.052 5.86e-11 -1.835
Metro_vs_DEMetro_Z 0.0 -2.014 0.0534 -0.368
Metro_vs_DEMetro_Z 0.3 -3.063 0.0047 -0.559
Metro_vs_DEMetro_Z 0.5 -0.870 0.391 -0.159
Metro_vs_DEMetro_Z 0.9 2.040 0.0506 0.372
Metro_vs_DEMetro_Z 0.99 8.383 3.07e-09 1.531
HMC_vs_SMC 0.0 -12.145 6.77e-13 -2.217
HMC_vs_SMC 0.3 -12.184 6.26e-13 -2.224
HMC_vs_SMC 0.5 -10.615 1.68e-11 -1.938
HMC_vs_SMC 0.9 -11.281 4.01e-12 -2.060
HMC_vs_SMC 0.99 -20.389 9.74e-19 -3.722
Metro_vs_SMC 0.0 -13.299 7.17e-14 -2.428
Metro_vs_SMC 0.3 -11.277 4.04e-12 -2.059
Metro_vs_SMC 0.5 -9.810 1.02e-10 -1.791
Metro_vs_SMC 0.9 -7.031 9.87e-08 -1.284
Metro_vs_SMC 0.99 1.336 0.192 0.244
HMC_vs_DEMetro_Z 0.0 -2.980 0.00578 -0.544
HMC_vs_DEMetro_Z 0.3 -8.140 5.63e-09 -1.486
HMC_vs_DEMetro_Z 0.5 -3.921 0.000495 -0.716
HMC_vs_DEMetro_Z 0.9 -2.982 0.00575 -0.544
HMC_vs_DEMetro_Z 0.99 -4.432 0.000122 -0.809
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.025 0.015 0.005 2.200
HMC 0.3 0.020 0.015 0.004 1.193
HMC 0.5 0.022 0.015 0.004 1.901
HMC 0.9 0.027 0.014 0.005 2.650
HMC 0.99 0.027 0.014 0.004 3.196
SMC 0.0 0.156 0.015 0.005 31.158
SMC 0.3 0.139 0.015 0.004 30.008
SMC 0.5 0.126 0.015 0.004 27.485
SMC 0.9 0.125 0.014 0.005 23.405
SMC 0.99 0.194 0.014 0.004 45.812
Metro 0.0 0.036 0.015 0.005 4.599
Metro 0.3 0.033 0.015 0.004 4.562
Metro 0.5 0.038 0.015 0.004 5.871
Metro 0.9 0.059 0.014 0.005 9.336
Metro 0.99 0.223 0.014 0.004 52.976
DEMetro_Z 0.0 0.044 0.015 0.005 6.476
DEMetro_Z 0.3 0.047 0.015 0.004 7.800
DEMetro_Z 0.5 0.041 0.015 0.004 6.531
DEMetro_Z 0.9 0.045 0.014 0.005 6.439
DEMetro_Z 0.99 0.052 0.014 0.004 9.704
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -0.181 0.857 -0.055
HMC 0.3 1.674 0.0998 0.496
HMC 0.5 1.828 0.0728 0.466
HMC 0.9 3.374 0.00192 2.470
HMC 0.99 2.152 0.0374 0.953
SMC 0.0 2.223 0.0306 0.715
SMC 0.3 0.968 0.337 0.231
SMC 0.5 1.612 0.113 0.453
SMC 0.9 1.448 0.155 0.573
SMC 0.99 3.517 0.00125 2.204
Metro 0.0 2.839 0.00737 1.549
Metro 0.3 1.335 0.192 4.217
Metro 0.5 1.334 0.193 4.007
Metro 0.9 5.182 1.31e-05 5.642
Metro 0.99 4.499 0.000101 21.123
DEMetro_Z 0.0 4.855 1.39e-05 1.763
DEMetro_Z 0.3 4.418 5.82e-05 1.584
DEMetro_Z 0.5 3.346 0.00205 2.332
DEMetro_Z 0.9 5.239 7.6e-06 3.035
DEMetro_Z 0.99 4.318 0.000132 2.924
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 -4.145 0.000269 -0.757
HMC_vs_DEMetro_Z 0.3 -3.361 0.00219 -0.614
HMC_vs_DEMetro_Z 0.5 -2.642 0.0131 -0.482
HMC_vs_DEMetro_Z 0.9 -0.662 0.513 -0.121
HMC_vs_DEMetro_Z 0.99 -2.303 0.0286 -0.420
Metro_vs_SMC 0.0 2.000 0.055 0.365
Metro_vs_SMC 0.3 1.270 0.214 0.232
Metro_vs_SMC 0.5 1.174 0.25 0.214
Metro_vs_SMC 0.9 4.346 0.000155 0.793
Metro_vs_SMC 0.99 3.908 0.000514 0.713
Metro_vs_DEMetro_Z 0.0 -0.361 0.721 -0.066
Metro_vs_DEMetro_Z 0.3 0.833 0.411 0.152
Metro_vs_DEMetro_Z 0.5 0.536 0.596 0.098
Metro_vs_DEMetro_Z 0.9 2.059 0.0486 0.376
Metro_vs_DEMetro_Z 0.99 3.814 0.000662 0.696
HMC_vs_Metro 0.0 -2.911 0.00686 -0.531
HMC_vs_Metro 0.3 -1.219 0.233 -0.223
HMC_vs_Metro 0.5 -1.182 0.247 -0.216
HMC_vs_Metro 0.9 -2.245 0.0325 -0.410
HMC_vs_Metro 0.99 -4.228 0.000215 -0.772
HMC_vs_SMC 0.0 -2.058 0.0487 -0.376
HMC_vs_SMC 0.3 1.017 0.317 0.186
HMC_vs_SMC 0.5 0.052 0.959 0.010
HMC_vs_SMC 0.9 2.603 0.0144 0.475
HMC_vs_SMC 0.99 -1.674 0.105 -0.306
DEMetro_Z_vs_SMC 0.0 2.609 0.0142 0.476
DEMetro_Z_vs_SMC 0.3 3.711 0.000872 0.677
DEMetro_Z_vs_SMC 0.5 2.661 0.0126 0.486
DEMetro_Z_vs_SMC 0.9 3.540 0.00137 0.646
DEMetro_Z_vs_SMC 0.99 0.742 0.464 0.135
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.063 0.065 0.042 -0.055
HMC 0.3 0.075 0.056 0.040 0.496
HMC 0.5 0.090 0.068 0.046 0.466
HMC 0.9 0.113 0.047 0.027 2.470
HMC 0.99 0.088 0.052 0.037 0.953
SMC 0.0 0.095 0.065 0.042 0.715
SMC 0.3 0.065 0.056 0.040 0.231
SMC 0.5 0.089 0.068 0.046 0.453
SMC 0.9 0.062 0.047 0.027 0.573
SMC 0.99 0.135 0.052 0.037 2.204
Metro 0.0 0.130 0.065 0.042 1.549
Metro 0.3 0.224 0.056 0.040 4.217
Metro 0.5 0.254 0.068 0.046 4.007
Metro 0.9 0.197 0.047 0.027 5.642
Metro 0.99 0.842 0.052 0.037 21.123
DEMetro_Z 0.0 0.139 0.065 0.042 1.763
DEMetro_Z 0.3 0.119 0.056 0.040 1.584
DEMetro_Z 0.5 0.177 0.068 0.046 2.332
DEMetro_Z 0.9 0.128 0.047 0.027 3.035
DEMetro_Z 0.99 0.162 0.052 0.037 2.924
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 -0.342 0.734 -0.109
HMC 0.3 1.389 0.173 0.694
HMC 0.5 0.415 0.68 0.104
HMC 0.9 0.591 0.557 0.181
HMC 0.99 -0.292 0.771 -0.078
SMC 0.0 -0.333 0.741 -0.064
SMC 0.3 0.617 0.54 0.176
SMC 0.5 0.407 0.686 0.101
SMC 0.9 -0.005 0.996 -0.001
SMC 0.99 1.197 0.236 0.298
Metro 0.0 -1.499 0.142 -0.293
Metro 0.3 1.007 0.322 2.604
Metro 0.5 1.119 0.272 0.891
Metro 0.9 0.002 0.998 0.000
Metro 0.99 0.512 0.61 0.132
DEMetro_Z 0.0 -1.510 0.14 -0.288
DEMetro_Z 0.3 0.962 0.341 0.306
DEMetro_Z 0.5 0.635 0.528 0.161
DEMetro_Z 0.9 -0.204 0.839 -0.045
DEMetro_Z 0.99 -0.073 0.942 -0.018
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 -0.162 0.872 -0.030
HMC_vs_SMC 0.3 1.171 0.251 0.214
HMC_vs_SMC 0.5 0.070 0.945 0.013
HMC_vs_SMC 0.9 0.745 0.462 0.136
HMC_vs_SMC 0.99 -1.858 0.0734 -0.339
Metro_vs_DEMetro_Z 0.0 -0.098 0.923 -0.018
Metro_vs_DEMetro_Z 0.3 0.906 0.372 0.165
Metro_vs_DEMetro_Z 0.5 0.976 0.337 0.178
Metro_vs_DEMetro_Z 0.9 1.099 0.281 0.201
Metro_vs_DEMetro_Z 0.99 1.130 0.268 0.206
HMC_vs_Metro 0.0 0.689 0.496 0.126
HMC_vs_Metro 0.3 -0.868 0.392 -0.158
HMC_vs_Metro 0.5 -1.039 0.307 -0.190
HMC_vs_Metro 0.9 0.868 0.393 0.158
HMC_vs_Metro 0.99 -1.328 0.195 -0.242
HMC_vs_DEMetro_Z 0.0 0.704 0.487 0.129
HMC_vs_DEMetro_Z 0.3 0.978 0.336 0.179
HMC_vs_DEMetro_Z 0.5 -1.214 0.235 -0.222
HMC_vs_DEMetro_Z 0.9 1.057 0.299 0.193
HMC_vs_DEMetro_Z 0.99 -0.428 0.671 -0.078
Metro_vs_SMC 0.0 -2.472 0.0195 -0.451
Metro_vs_SMC 0.3 0.944 0.353 0.172
Metro_vs_SMC 0.5 1.056 0.3 0.193
Metro_vs_SMC 0.9 0.016 0.987 0.003
Metro_vs_SMC 0.99 -0.905 0.373 -0.165
DEMetro_Z_vs_SMC 0.0 -2.678 0.0121 -0.489
DEMetro_Z_vs_SMC 0.3 1.001 0.325 0.183
DEMetro_Z_vs_SMC 0.5 1.418 0.167 0.259
DEMetro_Z_vs_SMC 0.9 -0.476 0.637 -0.087
DEMetro_Z_vs_SMC 0.99 -1.886 0.0694 -0.344
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 7.564 9.112 14.240 -0.109
HMC 0.3 8.152 4.697 4.977 0.694
HMC 0.5 12.319 9.883 23.480 0.104
HMC 0.9 6.706 5.328 7.624 0.181
HMC 0.99 5.450 6.084 8.146 -0.078
SMC 0.0 8.195 9.112 14.240 -0.064
SMC 0.3 5.571 4.697 4.977 0.176
SMC 0.5 12.253 9.883 23.480 0.101
SMC 0.9 5.320 5.328 7.624 -0.001
SMC 0.99 8.514 6.084 8.146 0.298
Metro 0.0 4.939 9.112 14.240 -0.293
Metro 0.3 17.656 4.697 4.977 2.604
Metro 0.5 30.792 9.883 23.480 0.891
Metro 0.9 5.331 5.328 7.624 0.000
Metro 0.99 7.158 6.084 8.146 0.132
DEMetro_Z 0.0 5.011 9.112 14.240 -0.288
DEMetro_Z 0.3 6.221 4.697 4.977 0.306
DEMetro_Z 0.5 13.653 9.883 23.480 0.161
DEMetro_Z 0.9 4.981 5.328 7.624 -0.045
DEMetro_Z 0.99 5.936 6.084 8.146 -0.018
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 1.831 0.0748 0.861
HMC 0.3 3.010 0.0049 1.943
HMC 0.5 3.896 0.00028 1.233
HMC 0.9 4.292 0.000126 2.324
HMC 0.99 4.542 5.81e-05 2.394
SMC 0.0 8.976 5.27e-10 12.383
SMC 0.3 6.883 1.12e-07 7.982
SMC 0.5 6.588 2.4e-07 6.906
SMC 0.9 7.004 7.89e-08 7.820
SMC 0.99 7.853 1.1e-08 22.812
Metro 0.0 4.805 2.98e-05 2.967
Metro 0.3 1.665 0.107 6.941
Metro 0.5 1.933 0.063 7.181
Metro 0.9 10.747 1.46e-12 6.608
Metro 0.99 5.854 2.37e-06 35.757
DEMetro_Z 0.0 10.716 2.23e-14 3.711
DEMetro_Z 0.3 11.182 4.92e-14 4.829
DEMetro_Z 0.5 7.139 3.35e-08 4.938
DEMetro_Z 0.9 8.839 2.77e-11 3.490
DEMetro_Z 0.99 5.256 1.11e-05 6.740
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 -1.126 0.27 -0.206
Metro_vs_DEMetro_Z 0.3 0.506 0.617 0.092
Metro_vs_DEMetro_Z 0.5 0.581 0.566 0.106
Metro_vs_DEMetro_Z 0.9 4.272 0.00019 0.780
Metro_vs_DEMetro_Z 0.99 4.630 7.08e-05 0.845
DEMetro_Z_vs_SMC 0.0 -6.110 1.18e-06 -1.115
DEMetro_Z_vs_SMC 0.3 -2.706 0.0113 -0.494
DEMetro_Z_vs_SMC 0.5 -1.877 0.0707 -0.343
DEMetro_Z_vs_SMC 0.9 -4.156 0.000261 -0.759
DEMetro_Z_vs_SMC 0.99 -4.857 3.78e-05 -0.887
HMC_vs_DEMetro_Z 0.0 -5.383 8.75e-06 -0.983
HMC_vs_DEMetro_Z 0.3 -4.262 0.000195 -0.778
HMC_vs_DEMetro_Z 0.5 -5.063 2.13e-05 -0.924
HMC_vs_DEMetro_Z 0.9 -2.628 0.0136 -0.480
HMC_vs_DEMetro_Z 0.99 -3.204 0.00329 -0.585
HMC_vs_Metro 0.0 -2.873 0.00753 -0.525
HMC_vs_Metro 0.3 -1.303 0.203 -0.238
HMC_vs_Metro 0.5 -1.592 0.122 -0.291
HMC_vs_Metro 0.9 -5.098 1.93e-05 -0.931
HMC_vs_Metro 0.99 -5.410 8.13e-06 -0.988
HMC_vs_SMC 0.0 -8.175 5.15e-09 -1.493
HMC_vs_SMC 0.3 -4.543 9.01e-05 -0.829
HMC_vs_SMC 0.5 -5.256 1.24e-05 -0.960
HMC_vs_SMC 0.9 -5.176 1.56e-05 -0.945
HMC_vs_SMC 0.99 -6.934 1.27e-07 -1.266
Metro_vs_SMC 0.0 -6.406 5.26e-07 -1.170
Metro_vs_SMC 0.3 -0.247 0.806 -0.045
Metro_vs_SMC 0.5 0.069 0.946 0.013
Metro_vs_SMC 0.9 -0.967 0.342 -0.177
Metro_vs_SMC 0.99 1.804 0.0817 0.329
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.154 0.124 0.035 0.861
HMC 0.3 0.169 0.116 0.027 1.943
HMC 0.5 0.164 0.120 0.036 1.233
HMC 0.9 0.193 0.115 0.034 2.324
HMC 0.99 0.167 0.109 0.024 2.394
SMC 0.0 0.557 0.124 0.035 12.383
SMC 0.3 0.333 0.116 0.027 7.982
SMC 0.5 0.370 0.120 0.036 6.906
SMC 0.9 0.377 0.115 0.034 7.820
SMC 0.99 0.664 0.109 0.024 22.812
Metro 0.0 0.228 0.124 0.035 2.967
Metro 0.3 0.304 0.116 0.027 6.941
Metro 0.5 0.380 0.120 0.036 7.181
Metro 0.9 0.337 0.115 0.034 6.608
Metro 0.99 0.979 0.109 0.024 35.757
DEMetro_Z 0.0 0.254 0.124 0.035 3.711
DEMetro_Z 0.3 0.247 0.116 0.027 4.829
DEMetro_Z 0.5 0.299 0.120 0.036 4.938
DEMetro_Z 0.9 0.232 0.115 0.034 3.490
DEMetro_Z 0.99 0.273 0.109 0.024 6.740
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 2.007 0.0499 0.623
HMC 0.3 3.234 0.00225 1.180
HMC 0.5 2.930 0.00502 0.927
HMC 0.9 6.390 6.2e-08 2.222
HMC 0.99 5.771 1.38e-06 3.151
SMC 0.0 12.604 2e-13 22.973
SMC 0.3 8.540 1.65e-09 13.080
SMC 0.5 7.913 8.91e-09 16.167
SMC 0.9 8.290 3.3e-09 15.010
SMC 0.99 9.871 8.39e-11 35.819
Metro 0.0 9.304 1.28e-11 4.089
Metro 0.3 6.252 4.61e-07 4.485
Metro 0.5 7.366 2.04e-08 5.659
Metro 0.9 7.933 6.97e-09 9.847
Metro 0.99 9.003 6.66e-10 56.660
DEMetro_Z 0.0 10.299 2.38e-12 5.509
DEMetro_Z 0.3 10.001 8.89e-12 6.010
DEMetro_Z 0.5 9.330 5.52e-11 5.682
DEMetro_Z 0.9 8.241 7.77e-10 4.459
DEMetro_Z 0.99 6.533 2.37e-07 5.451
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 -9.222 4.01e-10 -1.684
DEMetro_Z_vs_SMC 0.3 -4.313 0.00017 -0.787
DEMetro_Z_vs_SMC 0.5 -5.067 2.11e-05 -0.925
DEMetro_Z_vs_SMC 0.9 -6.114 1.17e-06 -1.116
DEMetro_Z_vs_SMC 0.99 -7.679 1.82e-08 -1.402
HMC_vs_Metro 0.0 -8.398 2.96e-09 -1.533
HMC_vs_Metro 0.3 -4.228 0.000215 -0.772
HMC_vs_Metro 0.5 -6.477 4.34e-07 -1.183
HMC_vs_Metro 0.9 -6.118 1.15e-06 -1.117
HMC_vs_Metro 0.99 -8.345 3.38e-09 -1.524
Metro_vs_DEMetro_Z 0.0 -2.143 0.0406 -0.391
Metro_vs_DEMetro_Z 0.3 -1.602 0.12 -0.293
Metro_vs_DEMetro_Z 0.5 -0.022 0.982 -0.004
Metro_vs_DEMetro_Z 0.9 3.742 0.000802 0.683
Metro_vs_DEMetro_Z 0.99 8.030 7.43e-09 1.466
HMC_vs_SMC 0.0 -13.048 1.15e-13 -2.382
HMC_vs_SMC 0.3 -7.645 1.98e-08 -1.396
HMC_vs_SMC 0.5 -7.565 2.44e-08 -1.381
HMC_vs_SMC 0.9 -7.094 8.35e-08 -1.295
HMC_vs_SMC 0.99 -8.768 1.19e-09 -1.601
Metro_vs_SMC 0.0 -10.400 2.69e-11 -1.899
Metro_vs_SMC 0.3 -5.629 4.42e-06 -1.028
Metro_vs_SMC 0.5 -4.993 2.58e-05 -0.912
Metro_vs_SMC 0.9 -2.335 0.0267 -0.426
Metro_vs_SMC 0.99 2.638 0.0133 0.482
HMC_vs_DEMetro_Z 0.0 -8.253 4.24e-09 -1.507
HMC_vs_DEMetro_Z 0.3 -7.004 1.06e-07 -1.279
HMC_vs_DEMetro_Z 0.5 -7.814 1.29e-08 -1.427
HMC_vs_DEMetro_Z 0.9 -3.674 0.000961 -0.671
HMC_vs_DEMetro_Z 0.99 -2.367 0.0248 -0.432
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.018 0.015 0.005 0.623
HMC 0.3 0.019 0.015 0.004 1.180
HMC 0.5 0.018 0.015 0.004 0.927
HMC 0.9 0.025 0.014 0.005 2.222
HMC 0.99 0.027 0.014 0.004 3.151
SMC 0.0 0.119 0.015 0.005 22.973
SMC 0.3 0.069 0.015 0.004 13.080
SMC 0.5 0.080 0.015 0.004 16.167
SMC 0.9 0.086 0.014 0.005 15.010
SMC 0.99 0.155 0.014 0.004 35.819
Metro 0.0 0.033 0.015 0.005 4.089
Metro 0.3 0.033 0.015 0.004 4.485
Metro 0.5 0.038 0.015 0.004 5.659
Metro 0.9 0.061 0.014 0.005 9.847
Metro 0.99 0.237 0.014 0.004 56.660
DEMetro_Z 0.0 0.040 0.015 0.005 5.509
DEMetro_Z 0.3 0.039 0.015 0.004 6.010
DEMetro_Z 0.5 0.038 0.015 0.004 5.682
DEMetro_Z 0.9 0.035 0.014 0.005 4.459
DEMetro_Z 0.99 0.036 0.014 0.004 5.451
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Trace Plots
Pooled
0.0 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.9 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.99 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
0.0 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.9 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.99 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
0.0
0.3
0.5
0.9
0.99
Chain
0.0
0.3
0.5
0.9
0.99

Vary_Correlation_with_high_Multimodality (Mixture, correlation, 30 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 6.218 8.66e-07 29.545
HMC 0.3 7.245 5.5e-08 32.338
HMC 0.5 7.671 1.81e-08 34.295
HMC 0.9 5.983 1.64e-06 25.060
HMC 0.99 7.119 7.57e-08 24.976
SMC 0.0 -0.250 0.803 -0.062
SMC 0.3 -1.160 0.251 -0.298
SMC 0.5 0.806 0.423 0.197
SMC 0.9 -1.132 0.263 -0.250
SMC 0.99 1.801 0.0771 0.515
Metro 0.0 7.119 7.66e-08 32.526
Metro 0.3 6.185 9.48e-07 29.400
Metro 0.5 7.722 1.59e-08 35.560
Metro 0.9 4.613 7.38e-05 20.369
Metro 0.99 6.575 3.28e-07 27.769
DEMetro_Z 0.0 6.306 6.76e-07 24.625
DEMetro_Z 0.3 6.026 1.46e-06 23.430
DEMetro_Z 0.5 7.334 4.28e-08 24.640
DEMetro_Z 0.9 4.443 0.000118 20.043
DEMetro_Z 0.99 6.379 5.59e-07 30.642
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 0.845 0.405 0.154
HMC_vs_DEMetro_Z 0.3 1.385 0.176 0.253
HMC_vs_DEMetro_Z 0.5 1.511 0.142 0.276
HMC_vs_DEMetro_Z 0.9 0.803 0.429 0.147
HMC_vs_DEMetro_Z 0.99 -0.999 0.326 -0.182
Metro_vs_SMC 0.0 7.110 7.99e-08 1.298
Metro_vs_SMC 0.3 6.156 1.04e-06 1.124
Metro_vs_SMC 0.5 7.767 1.45e-08 1.418
Metro_vs_SMC 0.9 4.655 6.6e-05 0.850
Metro_vs_SMC 0.99 6.416 5.12e-07 1.171
Metro_vs_DEMetro_Z 0.0 1.474 0.151 0.269
Metro_vs_DEMetro_Z 0.3 1.200 0.24 0.219
Metro_vs_DEMetro_Z 0.5 1.975 0.0579 0.360
Metro_vs_DEMetro_Z 0.9 0.052 0.959 0.009
Metro_vs_DEMetro_Z 0.99 -0.468 0.643 -0.085
HMC_vs_Metro 0.0 -0.759 0.454 -0.139
HMC_vs_Metro 0.3 0.612 0.545 0.112
HMC_vs_Metro 0.5 -0.229 0.821 -0.042
HMC_vs_Metro 0.9 1.148 0.26 0.210
HMC_vs_Metro 0.99 -0.465 0.645 -0.085
HMC_vs_SMC 0.0 6.220 8.72e-07 1.136
HMC_vs_SMC 0.3 7.289 5e-08 1.331
HMC_vs_SMC 0.5 7.651 1.95e-08 1.397
HMC_vs_SMC 0.9 5.999 1.6e-06 1.095
HMC_vs_SMC 0.99 6.930 1.29e-07 1.265
DEMetro_Z_vs_SMC 0.0 6.352 6.09e-07 1.160
DEMetro_Z_vs_SMC 0.3 6.048 1.4e-06 1.104
DEMetro_Z_vs_SMC 0.5 7.265 5.32e-08 1.326
DEMetro_Z_vs_SMC 0.9 4.548 8.9e-05 0.830
DEMetro_Z_vs_SMC 0.99 6.218 8.78e-07 1.135
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 1.697 0.080 0.055 29.545
HMC 0.3 2.175 0.089 0.065 32.338
HMC 0.5 2.384 0.091 0.067 34.295
HMC 0.9 1.939 0.089 0.074 25.060
HMC 0.99 1.646 0.075 0.063 24.976
SMC 0.0 0.077 0.080 0.055 -0.062
SMC 0.3 0.069 0.089 0.065 -0.298
SMC 0.5 0.105 0.091 0.067 0.197
SMC 0.9 0.070 0.089 0.074 -0.250
SMC 0.99 0.107 0.075 0.063 0.515
Metro 0.0 1.860 0.080 0.055 32.526
Metro 0.3 1.985 0.089 0.065 29.400
Metro 0.5 2.469 0.091 0.067 35.560
Metro 0.9 1.593 0.089 0.074 20.369
Metro 0.99 1.822 0.075 0.063 27.769
DEMetro_Z 0.0 1.428 0.080 0.055 24.625
DEMetro_Z 0.3 1.600 0.089 0.065 23.430
DEMetro_Z 0.5 1.739 0.091 0.067 24.640
DEMetro_Z 0.9 1.568 0.089 0.074 20.043
DEMetro_Z 0.99 2.002 0.075 0.063 30.642
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 4.447 0.000117 56.425
HMC 0.3 5.133 1.75e-05 87.867
HMC 0.5 5.482 6.64e-06 83.152
HMC 0.9 4.573 8.3e-05 74.985
HMC 0.99 5.378 8.85e-06 41.853
SMC 0.0 -0.265 0.792 -0.070
SMC 0.3 0.773 0.443 0.220
SMC 0.5 -0.939 0.352 -0.206
SMC 0.9 1.773 0.0815 0.447
SMC 0.99 0.916 0.364 0.249
Metro 0.0 4.907 3.28e-05 60.761
Metro 0.3 4.643 6.83e-05 82.332
Metro 0.5 5.717 3.47e-06 89.388
Metro 0.9 4.001 0.000399 67.833
Metro 0.99 5.404 8.25e-06 66.127
DEMetro_Z 0.0 4.066 0.000334 38.398
DEMetro_Z 0.3 3.957 0.000449 54.882
DEMetro_Z 0.5 4.216 0.000222 44.452
DEMetro_Z 0.9 3.899 0.000526 66.626
DEMetro_Z 0.99 4.761 4.93e-05 69.954
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 4.453 0.000116 0.813
HMC_vs_SMC 0.3 5.121 1.81e-05 0.935
HMC_vs_SMC 0.5 5.501 6.32e-06 1.004
HMC_vs_SMC 0.9 4.544 8.99e-05 0.830
HMC_vs_SMC 0.99 5.357 9.42e-06 0.978
Metro_vs_DEMetro_Z 0.0 1.931 0.0633 0.353
Metro_vs_DEMetro_Z 0.3 1.505 0.143 0.275
Metro_vs_DEMetro_Z 0.5 2.419 0.0221 0.442
Metro_vs_DEMetro_Z 0.9 0.048 0.962 0.009
Metro_vs_DEMetro_Z 0.99 -0.215 0.831 -0.039
HMC_vs_Metro 0.0 -0.426 0.673 -0.078
HMC_vs_Metro 0.3 0.300 0.766 0.055
HMC_vs_Metro 0.5 -0.318 0.753 -0.058
HMC_vs_Metro 0.9 0.471 0.641 0.086
HMC_vs_Metro 0.99 -1.537 0.135 -0.281
HMC_vs_DEMetro_Z 0.0 1.179 0.248 0.215
HMC_vs_DEMetro_Z 0.3 1.342 0.19 0.245
HMC_vs_DEMetro_Z 0.5 1.816 0.0798 0.331
HMC_vs_DEMetro_Z 0.9 0.349 0.73 0.064
HMC_vs_DEMetro_Z 0.99 -1.644 0.111 -0.300
Metro_vs_SMC 0.0 4.908 3.28e-05 0.896
Metro_vs_SMC 0.3 4.642 6.85e-05 0.848
Metro_vs_SMC 0.5 5.732 3.33e-06 1.047
Metro_vs_SMC 0.9 3.973 0.00043 0.725
Metro_vs_SMC 0.99 5.396 8.44e-06 0.985
DEMetro_Z_vs_SMC 0.0 4.072 0.000329 0.743
DEMetro_Z_vs_SMC 0.3 3.954 0.000454 0.722
DEMetro_Z_vs_SMC 0.5 4.230 0.000214 0.772
DEMetro_Z_vs_SMC 0.9 3.866 0.000574 0.706
DEMetro_Z_vs_SMC 0.99 4.750 5.09e-05 0.867
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 7.044 0.169 0.122 56.425
HMC 0.3 10.033 0.159 0.112 87.867
HMC 0.5 11.699 0.179 0.139 83.152
HMC 0.9 9.313 0.163 0.122 74.985
HMC 0.99 5.790 0.181 0.134 41.853
SMC 0.0 0.161 0.169 0.122 -0.070
SMC 0.3 0.184 0.159 0.112 0.220
SMC 0.5 0.150 0.179 0.139 -0.206
SMC 0.9 0.217 0.163 0.122 0.447
SMC 0.99 0.214 0.181 0.134 0.249
Metro 0.0 7.572 0.169 0.122 60.761
Metro 0.3 9.411 0.159 0.112 82.332
Metro 0.5 12.563 0.179 0.139 89.388
Metro 0.9 8.440 0.163 0.122 67.833
Metro 0.99 9.043 0.181 0.134 66.127
DEMetro_Z 0.0 4.848 0.169 0.122 38.398
DEMetro_Z 0.3 6.326 0.159 0.112 54.882
DEMetro_Z 0.5 6.337 0.179 0.139 44.452
DEMetro_Z 0.9 8.293 0.163 0.122 66.626
DEMetro_Z 0.99 9.556 0.181 0.134 69.954
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 6.106 1.18e-06 31.933
HMC 0.3 7.086 8.39e-08 36.402
HMC 0.5 7.614 2.11e-08 39.150
HMC 0.9 5.832 2.49e-06 25.986
HMC 0.99 7.238 5.54e-08 26.072
SMC 0.0 0.140 0.889 0.035
SMC 0.3 -1.019 0.312 -0.251
SMC 0.5 0.585 0.561 0.146
SMC 0.9 -1.105 0.274 -0.242
SMC 0.99 2.106 0.0398 0.611
Metro 0.0 7.030 9.76e-08 37.178
Metro 0.3 6.200 9.11e-07 32.302
Metro 0.5 7.774 1.4e-08 40.682
Metro 0.9 4.645 6.76e-05 20.949
Metro 0.99 6.953 1.19e-07 29.894
DEMetro_Z 0.0 6.339 6.2e-07 27.122
DEMetro_Z 0.3 6.031 1.44e-06 25.401
DEMetro_Z 0.5 7.343 4.22e-08 27.798
DEMetro_Z 0.9 4.557 8.62e-05 20.570
DEMetro_Z 0.99 6.478 4.28e-07 32.526
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 1.736 0.0932 0.317
Metro_vs_DEMetro_Z 0.3 1.319 0.198 0.241
Metro_vs_DEMetro_Z 0.5 2.083 0.0462 0.380
Metro_vs_DEMetro_Z 0.9 0.059 0.953 0.011
Metro_vs_DEMetro_Z 0.99 -0.419 0.678 -0.077
DEMetro_Z_vs_SMC 0.0 6.361 5.94e-07 1.161
DEMetro_Z_vs_SMC 0.3 6.053 1.38e-06 1.105
DEMetro_Z_vs_SMC 0.5 7.284 5.06e-08 1.330
DEMetro_Z_vs_SMC 0.9 4.647 6.76e-05 0.848
DEMetro_Z_vs_SMC 0.99 6.300 7.02e-07 1.150
HMC_vs_DEMetro_Z 0.0 0.768 0.449 0.140
HMC_vs_DEMetro_Z 0.3 1.528 0.137 0.279
HMC_vs_DEMetro_Z 0.5 1.577 0.126 0.288
HMC_vs_DEMetro_Z 0.9 0.846 0.404 0.155
HMC_vs_DEMetro_Z 0.99 -1.123 0.271 -0.205
HMC_vs_Metro 0.0 -1.206 0.238 -0.220
HMC_vs_Metro 0.3 0.727 0.473 0.133
HMC_vs_Metro 0.5 -0.236 0.815 -0.043
HMC_vs_Metro 0.9 1.205 0.238 0.220
HMC_vs_Metro 0.99 -0.621 0.54 -0.113
HMC_vs_SMC 0.0 6.100 1.21e-06 1.114
HMC_vs_SMC 0.3 7.123 7.73e-08 1.300
HMC_vs_SMC 0.5 7.600 2.23e-08 1.387
HMC_vs_SMC 0.9 5.840 2.47e-06 1.066
HMC_vs_SMC 0.99 7.026 9.98e-08 1.283
Metro_vs_SMC 0.0 7.012 1.04e-07 1.280
Metro_vs_SMC 0.3 6.184 9.63e-07 1.129
Metro_vs_SMC 0.5 7.824 1.25e-08 1.428
Metro_vs_SMC 0.9 4.675 6.25e-05 0.854
Metro_vs_SMC 0.99 6.788 1.88e-07 1.239
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 1.500 0.089 0.044 31.933
HMC 0.3 2.043 0.096 0.053 36.402
HMC 0.5 2.149 0.098 0.052 39.150
HMC 0.9 1.785 0.098 0.065 25.986
HMC 0.99 1.479 0.085 0.053 26.072
SMC 0.0 0.090 0.089 0.044 0.035
SMC 0.3 0.082 0.096 0.053 -0.251
SMC 0.5 0.105 0.098 0.052 0.146
SMC 0.9 0.082 0.098 0.065 -0.242
SMC 0.99 0.117 0.085 0.053 0.611
Metro 0.0 1.732 0.089 0.044 37.178
Metro 0.3 1.824 0.096 0.053 32.302
Metro 0.5 2.230 0.098 0.052 40.682
Metro 0.9 1.458 0.098 0.065 20.949
Metro 0.99 1.684 0.085 0.053 29.894
DEMetro_Z 0.0 1.287 0.089 0.044 27.122
DEMetro_Z 0.3 1.454 0.096 0.053 25.401
DEMetro_Z 0.5 1.554 0.098 0.052 27.798
DEMetro_Z 0.9 1.434 0.098 0.065 20.570
DEMetro_Z 0.99 1.824 0.085 0.053 32.526
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 6.379 5.6e-07 33.225
HMC 0.3 7.490 2.89e-08 32.546
HMC 0.5 7.897 1.02e-08 36.512
HMC 0.9 6.141 1.07e-06 29.014
HMC 0.99 7.182 6.49e-08 31.319
SMC 0.0 -0.265 0.792 -0.067
SMC 0.3 -0.798 0.428 -0.193
SMC 0.5 0.679 0.5 0.167
SMC 0.9 -1.044 0.301 -0.230
SMC 0.99 2.015 0.0488 0.591
Metro 0.0 7.290 4.91e-08 36.624
Metro 0.3 6.398 5.3e-07 29.385
Metro 0.5 8.019 7.48e-09 38.137
Metro 0.9 4.835 3.99e-05 23.835
Metro 0.99 7.071 8.73e-08 36.130
DEMetro_Z 0.0 6.472 4.32e-07 28.033
DEMetro_Z 0.3 6.259 7.69e-07 24.071
DEMetro_Z 0.5 7.634 1.97e-08 26.933
DEMetro_Z 0.9 4.579 8.12e-05 23.269
DEMetro_Z 0.99 6.678 2.5e-07 37.984
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 6.522 3.84e-07 1.191
DEMetro_Z_vs_SMC 0.3 6.269 7.64e-07 1.144
DEMetro_Z_vs_SMC 0.5 7.563 2.45e-08 1.381
DEMetro_Z_vs_SMC 0.9 4.662 6.48e-05 0.851
DEMetro_Z_vs_SMC 0.99 6.533 3.73e-07 1.193
HMC_vs_Metro 0.0 -0.769 0.448 -0.140
HMC_vs_Metro 0.3 0.671 0.508 0.122
HMC_vs_Metro 0.5 -0.286 0.777 -0.052
HMC_vs_Metro 0.9 1.143 0.263 0.209
HMC_vs_Metro 0.99 -0.654 0.518 -0.119
Metro_vs_DEMetro_Z 0.0 1.448 0.158 0.264
Metro_vs_DEMetro_Z 0.3 1.094 0.283 0.200
Metro_vs_DEMetro_Z 0.5 1.946 0.0613 0.355
Metro_vs_DEMetro_Z 0.9 0.080 0.937 0.015
Metro_vs_DEMetro_Z 0.99 -0.246 0.807 -0.045
HMC_vs_SMC 0.0 6.392 5.46e-07 1.167
HMC_vs_SMC 0.3 7.508 2.82e-08 1.371
HMC_vs_SMC 0.5 7.898 1.04e-08 1.442
HMC_vs_SMC 0.9 6.140 1.09e-06 1.121
HMC_vs_SMC 0.99 6.999 1.07e-07 1.278
Metro_vs_SMC 0.0 7.288 5.01e-08 1.331
Metro_vs_SMC 0.3 6.364 5.89e-07 1.162
Metro_vs_SMC 0.5 8.059 6.9e-09 1.471
Metro_vs_SMC 0.9 4.861 3.73e-05 0.887
Metro_vs_SMC 0.99 6.922 1.32e-07 1.264
HMC_vs_DEMetro_Z 0.0 0.812 0.423 0.148
HMC_vs_DEMetro_Z 0.3 1.342 0.19 0.245
HMC_vs_DEMetro_Z 0.5 1.439 0.161 0.263
HMC_vs_DEMetro_Z 0.9 0.811 0.424 0.148
HMC_vs_DEMetro_Z 0.99 -0.984 0.333 -0.180
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.236 0.011 0.007 33.225
HMC 0.3 0.303 0.012 0.009 32.546
HMC 0.5 0.330 0.012 0.009 36.512
HMC 0.9 0.270 0.012 0.009 29.014
HMC 0.99 0.235 0.010 0.007 31.319
SMC 0.0 0.011 0.011 0.007 -0.067
SMC 0.3 0.010 0.012 0.009 -0.193
SMC 0.5 0.014 0.012 0.009 0.167
SMC 0.9 0.009 0.012 0.009 -0.230
SMC 0.99 0.014 0.010 0.007 0.591
Metro 0.0 0.259 0.011 0.007 36.624
Metro 0.3 0.274 0.012 0.009 29.385
Metro 0.5 0.345 0.012 0.009 38.137
Metro 0.9 0.224 0.012 0.009 23.835
Metro 0.99 0.269 0.010 0.007 36.130
DEMetro_Z 0.0 0.201 0.011 0.007 28.033
DEMetro_Z 0.3 0.227 0.012 0.009 24.071
DEMetro_Z 0.5 0.247 0.012 0.009 26.933
DEMetro_Z 0.9 0.219 0.012 0.009 23.269
DEMetro_Z 0.99 0.283 0.010 0.007 37.984
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 275.846 1.56e-87 82.223
HMC 0.3 263.929 7.48e-91 69.822
HMC 0.5 250.758 2.68e-89 67.366
HMC 0.9 250.576 1.13e-88 61.181
HMC 0.99 254.737 3.53e-88 71.859
SMC 0.0 0.973 0.335 0.273
SMC 0.3 -0.433 0.666 -0.114
SMC 0.5 0.267 0.791 0.064
SMC 0.9 0.140 0.89 0.034
SMC 0.99 0.538 0.592 0.134
Metro 0.0 264.816 1.94e-84 82.116
Metro 0.3 42.949 2.36e-28 67.712
Metro 0.5 262.219 7.36e-91 67.529
Metro 0.9 203.290 5.09e-80 60.959
Metro 0.99 96.507 1.08e-41 72.241
DEMetro_Z 0.0 8.099 6.18e-09 55.677
DEMetro_Z 0.3 13.169 8.67e-14 58.106
DEMetro_Z 0.5 265.204 4.31e-91 67.582
DEMetro_Z 0.9 235.667 3.67e-88 61.250
DEMetro_Z 0.99 261.612 8.9e-90 71.858
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0.0 3.802 0.000683 0.694
HMC_vs_DEMetro_Z 0.3 2.650 0.0129 0.484
HMC_vs_DEMetro_Z 0.5 -1.062 0.297 -0.194
HMC_vs_DEMetro_Z 0.9 -0.463 0.647 -0.085
HMC_vs_DEMetro_Z 0.99 0.004 0.997 0.001
Metro_vs_SMC 0.0 246.149 1.06e-49 44.940
Metro_vs_SMC 0.3 41.692 1.95e-27 7.612
Metro_vs_SMC 0.5 298.268 4.04e-52 54.456
Metro_vs_SMC 0.9 208.832 1.24e-47 38.127
Metro_vs_SMC 0.99 89.153 6.25e-37 16.277
Metro_vs_DEMetro_Z 0.0 3.787 0.000712 0.691
Metro_vs_DEMetro_Z 0.3 2.191 0.0366 0.400
Metro_vs_DEMetro_Z 0.5 -0.302 0.765 -0.055
Metro_vs_DEMetro_Z 0.9 -1.236 0.226 -0.226
Metro_vs_DEMetro_Z 0.99 0.533 0.598 0.097
HMC_vs_Metro 0.0 1.260 0.218 0.230
HMC_vs_Metro 0.3 1.328 0.195 0.242
HMC_vs_Metro 0.5 -1.257 0.219 -0.230
HMC_vs_Metro 0.9 1.013 0.32 0.185
HMC_vs_Metro 0.99 -0.485 0.631 -0.089
HMC_vs_SMC 0.0 261.355 1.86e-50 47.717
HMC_vs_SMC 0.3 244.286 1.32e-49 44.600
HMC_vs_SMC 0.5 293.623 6.36e-52 53.608
HMC_vs_SMC 0.9 256.870 3.07e-50 46.898
HMC_vs_SMC 0.99 286.897 1.25e-51 52.380
DEMetro_Z_vs_SMC 0.0 7.965 8.75e-09 1.454
DEMetro_Z_vs_SMC 0.3 13.170 9.15e-14 2.405
DEMetro_Z_vs_SMC 0.5 319.609 5.45e-53 58.352
DEMetro_Z_vs_SMC 0.9 274.684 4.4e-51 50.150
DEMetro_Z_vs_SMC 0.99 246.672 9.94e-50 45.036
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 4.580 0.080 0.055 82.223
HMC 0.3 4.593 0.089 0.065 69.822
HMC 0.5 4.595 0.091 0.067 67.366
HMC 0.9 4.606 0.089 0.074 61.181
HMC 0.99 4.595 0.075 0.063 71.859
SMC 0.0 0.095 0.080 0.055 0.273
SMC 0.3 0.081 0.089 0.065 -0.114
SMC 0.5 0.096 0.091 0.067 0.064
SMC 0.9 0.091 0.089 0.074 0.034
SMC 0.99 0.083 0.075 0.063 0.134
Metro 0.0 4.574 0.080 0.055 82.116
Metro 0.3 4.456 0.089 0.065 67.712
Metro 0.5 4.606 0.091 0.067 67.529
Metro 0.9 4.589 0.089 0.074 60.959
Metro 0.99 4.619 0.075 0.063 72.241
DEMetro_Z 0.0 3.127 0.080 0.055 55.677
DEMetro_Z 0.3 3.837 0.089 0.065 58.106
DEMetro_Z 0.5 4.610 0.091 0.067 67.582
DEMetro_Z 0.9 4.611 0.089 0.074 61.250
DEMetro_Z 0.99 4.595 0.075 0.063 71.858
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 908.425 1.49e-121 243.815
HMC 0.3 874.472 7.84e-114 264.448
HMC 0.5 812.539 3.67e-119 214.267
HMC 0.9 852.375 3.05e-117 242.860
HMC 0.99 779.715 3.18e-115 221.554
SMC 0.0 -0.002 0.998 -0.001
SMC 0.3 0.569 0.571 0.144
SMC 0.5 -0.034 0.973 -0.009
SMC 0.9 -0.248 0.805 -0.059
SMC 0.99 0.387 0.701 0.099
Metro 0.0 877.976 2.32e-119 243.793
Metro 0.3 28.935 5.88e-23 252.140
Metro 0.5 782.484 4.14e-117 214.340
Metro 0.9 802.938 9.21e-112 243.041
Metro 0.99 456.962 4.04e-73 222.229
DEMetro_Z 0.0 7.753 1.5e-08 163.501
DEMetro_Z 0.3 11.305 3.79e-12 213.934
DEMetro_Z 0.5 830.904 6.67e-120 214.163
DEMetro_Z 0.9 838.288 9.07e-116 243.021
DEMetro_Z 0.99 757.024 1.04e-112 221.514
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0.0 1009.182 1.8e-67 184.251
HMC_vs_SMC 0.3 1234.659 5.21e-70 225.417
HMC_vs_SMC 0.5 702.118 6.69e-63 128.189
HMC_vs_SMC 0.9 872.189 1.24e-65 159.239
HMC_vs_SMC 0.99 704.252 6.13e-63 128.578
Metro_vs_DEMetro_Z 0.0 3.811 0.000666 0.696
Metro_vs_DEMetro_Z 0.3 1.973 0.0581 0.360
Metro_vs_DEMetro_Z 0.5 2.761 0.00989 0.504
Metro_vs_DEMetro_Z 0.9 0.150 0.882 0.027
Metro_vs_DEMetro_Z 0.99 2.007 0.0541 0.366
HMC_vs_Metro 0.0 0.470 0.642 0.086
HMC_vs_Metro 0.3 1.418 0.167 0.259
HMC_vs_Metro 0.5 -1.177 0.249 -0.215
HMC_vs_Metro 0.9 -1.385 0.177 -0.253
HMC_vs_Metro 0.99 -1.925 0.064 -0.352
HMC_vs_DEMetro_Z 0.0 3.811 0.000666 0.696
HMC_vs_DEMetro_Z 0.3 2.683 0.0119 0.490
HMC_vs_DEMetro_Z 0.5 1.839 0.0762 0.336
HMC_vs_DEMetro_Z 0.9 -2.006 0.0542 -0.366
HMC_vs_DEMetro_Z 0.99 0.480 0.635 0.088
Metro_vs_SMC 0.0 958.403 8.07e-67 174.980
Metro_vs_SMC 0.3 28.896 6.3e-23 5.276
Metro_vs_SMC 0.5 697.736 8.02e-63 127.389
Metro_vs_SMC 0.9 802.583 1.38e-64 146.531
Metro_vs_SMC 0.99 431.063 9.31e-57 78.701
DEMetro_Z_vs_SMC 0.0 7.729 1.6e-08 1.411
DEMetro_Z_vs_SMC 0.3 11.312 3.75e-12 2.065
DEMetro_Z_vs_SMC 0.5 737.888 1.58e-63 134.719
DEMetro_Z_vs_SMC 0.9 834.711 4.44e-65 152.397
DEMetro_Z_vs_SMC 0.99 721.560 3.03e-63 131.738
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 29.874 0.169 0.122 243.815
HMC 0.3 29.875 0.159 0.112 264.448
HMC 0.5 29.865 0.179 0.139 214.267
HMC 0.9 29.799 0.163 0.122 242.860
HMC 0.99 29.873 0.181 0.134 221.554
SMC 0.0 0.169 0.169 0.122 -0.001
SMC 0.3 0.175 0.159 0.112 0.144
SMC 0.5 0.177 0.179 0.139 -0.009
SMC 0.9 0.155 0.163 0.122 -0.059
SMC 0.99 0.194 0.181 0.134 0.099
Metro 0.0 29.872 0.169 0.122 243.793
Metro 0.3 28.492 0.159 0.112 252.140
Metro 0.5 29.875 0.179 0.139 214.340
Metro 0.9 29.821 0.163 0.122 243.041
Metro 0.99 29.963 0.181 0.134 222.229
DEMetro_Z 0.0 20.089 0.169 0.122 163.501
DEMetro_Z 0.3 24.199 0.159 0.112 213.934
DEMetro_Z 0.5 29.850 0.179 0.139 214.163
DEMetro_Z 0.9 29.818 0.163 0.122 243.021
DEMetro_Z 0.99 29.867 0.181 0.134 221.514
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 75.274 4.69e-36 91.543
HMC 0.3 74.113 1.99e-36 74.755
HMC 0.5 73.658 3.31e-36 77.223
HMC 0.9 72.751 5.75e-37 61.484
HMC 0.99 58.198 1.46e-32 75.134
SMC 0.0 1.192 0.238 0.345
SMC 0.3 -0.217 0.829 -0.054
SMC 0.5 0.560 0.577 0.137
SMC 0.9 -0.093 0.926 -0.022
SMC 0.99 0.513 0.61 0.126
Metro 0.0 71.213 3.21e-35 90.677
Metro 0.3 39.593 3.36e-27 71.003
Metro 0.5 58.416 1.45e-32 77.183
Metro 0.9 67.012 1.78e-35 61.144
Metro 0.99 53.398 2.85e-31 76.341
DEMetro_Z 0.0 8.148 5.47e-09 61.714
DEMetro_Z 0.3 12.906 1.45e-13 63.078
DEMetro_Z 0.5 81.816 4.17e-38 75.875
DEMetro_Z 0.9 82.010 2.77e-39 62.347
DEMetro_Z 0.99 63.878 5.92e-34 76.119
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0.0 3.826 0.00064 0.699
Metro_vs_DEMetro_Z 0.3 1.586 0.124 0.290
Metro_vs_DEMetro_Z 0.5 0.771 0.447 0.141
Metro_vs_DEMetro_Z 0.9 -1.151 0.259 -0.210
Metro_vs_DEMetro_Z 0.99 0.126 0.9 0.023
DEMetro_Z_vs_SMC 0.0 8.004 7.94e-09 1.461
DEMetro_Z_vs_SMC 0.3 12.907 1.51e-13 2.357
DEMetro_Z_vs_SMC 0.5 83.039 4.86e-36 15.161
DEMetro_Z_vs_SMC 0.9 82.792 5.3e-36 15.116
DEMetro_Z_vs_SMC 0.99 64.641 6.68e-33 11.802
HMC_vs_DEMetro_Z 0.0 3.972 0.000431 0.725
HMC_vs_DEMetro_Z 0.3 2.284 0.0299 0.417
HMC_vs_DEMetro_Z 0.5 0.982 0.334 0.179
HMC_vs_DEMetro_Z 0.9 -0.867 0.393 -0.158
HMC_vs_DEMetro_Z 0.99 -0.602 0.552 -0.110
HMC_vs_Metro 0.0 0.521 0.606 0.095
HMC_vs_Metro 0.3 1.785 0.0847 0.326
HMC_vs_Metro 0.5 0.022 0.982 0.004
HMC_vs_Metro 0.9 0.269 0.79 0.049
HMC_vs_Metro 0.99 -0.735 0.468 -0.134
HMC_vs_SMC 0.0 73.943 1.39e-34 13.500
HMC_vs_SMC 0.3 75.088 8.89e-35 13.709
HMC_vs_SMC 0.5 73.512 1.64e-34 13.421
HMC_vs_SMC 0.9 73.503 1.65e-34 13.420
HMC_vs_SMC 0.99 58.485 1.19e-31 10.678
Metro_vs_SMC 0.0 69.259 9.15e-34 12.645
Metro_vs_SMC 0.3 39.128 1.19e-26 7.144
Metro_vs_SMC 0.5 56.669 2.95e-31 10.346
Metro_vs_SMC 0.9 65.415 4.74e-33 11.943
Metro_vs_SMC 0.99 53.283 1.73e-30 9.728
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 4.134 0.089 0.044 91.543
HMC 0.3 4.094 0.096 0.053 74.755
HMC 0.5 4.145 0.098 0.052 77.223
HMC 0.9 4.091 0.098 0.065 61.484
HMC 0.99 4.103 0.085 0.053 75.134
SMC 0.0 0.104 0.089 0.044 0.345
SMC 0.3 0.093 0.096 0.053 -0.054
SMC 0.5 0.105 0.098 0.052 0.137
SMC 0.9 0.097 0.098 0.065 -0.022
SMC 0.99 0.092 0.085 0.053 0.126
Metro 0.0 4.096 0.089 0.044 90.677
Metro 0.3 3.893 0.096 0.053 71.003
Metro 0.5 4.143 0.098 0.052 77.183
Metro 0.9 4.068 0.098 0.065 61.144
Metro 0.99 4.168 0.085 0.053 76.341
DEMetro_Z 0.0 2.816 0.089 0.044 61.714
DEMetro_Z 0.3 3.470 0.096 0.053 63.078
DEMetro_Z 0.5 4.074 0.098 0.052 75.875
DEMetro_Z 0.9 4.147 0.098 0.065 62.347
DEMetro_Z 0.99 4.156 0.085 0.053 76.119
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 0.0 146.592 4.58e-50 88.972
HMC 0.3 148.567 6.03e-56 68.158
HMC 0.5 170.511 7.52e-62 70.052
HMC 0.9 145.397 9.83e-55 68.902
HMC 0.99 167.559 3.88e-55 86.191
SMC 0.0 1.049 0.299 0.296
SMC 0.3 -0.039 0.969 -0.010
SMC 0.5 0.604 0.548 0.144
SMC 0.9 0.232 0.817 0.059
SMC 0.99 0.682 0.498 0.180
Metro 0.0 145.287 1.09e-49 89.690
Metro 0.3 44.793 5.75e-29 66.269
Metro 0.5 136.549 5.83e-52 69.820
Metro 0.9 151.264 1.9e-56 68.913
Metro 0.99 136.023 5.04e-48 88.494
DEMetro_Z 0.0 8.138 5.6e-09 60.493
DEMetro_Z 0.3 13.324 6.43e-14 56.483
DEMetro_Z 0.5 181.411 5.76e-66 69.107
DEMetro_Z 0.9 154.868 2.29e-57 69.295
DEMetro_Z 0.99 152.839 4.44e-52 85.207
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0.0 8.012 7.77e-09 1.463
DEMetro_Z_vs_SMC 0.3 13.329 6.78e-14 2.434
DEMetro_Z_vs_SMC 0.5 187.405 2.86e-46 34.215
DEMetro_Z_vs_SMC 0.9 151.843 1.27e-43 27.723
DEMetro_Z_vs_SMC 0.99 138.194 1.94e-42 25.231
HMC_vs_Metro 0.0 -0.894 0.379 -0.163
HMC_vs_Metro 0.3 1.143 0.262 0.209
HMC_vs_Metro 0.5 0.414 0.682 0.076
HMC_vs_Metro 0.9 -0.019 0.985 -0.004
HMC_vs_Metro 0.99 -3.171 0.00357 -0.579
Metro_vs_DEMetro_Z 0.0 3.919 0.000498 0.715
Metro_vs_DEMetro_Z 0.3 2.283 0.03 0.417
Metro_vs_DEMetro_Z 0.5 1.153 0.258 0.211
Metro_vs_DEMetro_Z 0.9 -0.737 0.467 -0.135
Metro_vs_DEMetro_Z 0.99 3.562 0.0013 0.650
HMC_vs_SMC 0.0 154.510 7.67e-44 28.209
HMC_vs_SMC 0.3 149.219 2.1e-43 27.243
HMC_vs_SMC 0.5 191.929 1.43e-46 35.041
HMC_vs_SMC 0.9 146.969 3.27e-43 26.833
HMC_vs_SMC 0.99 169.879 4.92e-45 31.015
Metro_vs_SMC 0.0 150.444 1.66e-43 27.467
Metro_vs_SMC 0.3 43.848 4.61e-28 8.005
Metro_vs_SMC 0.5 149.020 2.19e-43 27.207
Metro_vs_SMC 0.9 154.010 8.42e-44 28.118
Metro_vs_SMC 0.99 144.032 5.86e-43 26.297
HMC_vs_DEMetro_Z 0.0 3.794 0.000697 0.693
HMC_vs_DEMetro_Z 0.3 2.769 0.00969 0.506
HMC_vs_DEMetro_Z 0.5 1.826 0.0782 0.333
HMC_vs_DEMetro_Z 0.9 -0.730 0.471 -0.133
HMC_vs_DEMetro_Z 0.99 1.689 0.102 0.308
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 0.0 0.613 0.011 0.007 88.972
HMC 0.3 0.621 0.012 0.009 68.158
HMC 0.5 0.623 0.012 0.009 70.052
HMC 0.9 0.626 0.012 0.009 68.902
HMC 0.99 0.629 0.010 0.007 86.191
SMC 0.0 0.013 0.011 0.007 0.296
SMC 0.3 0.012 0.012 0.009 -0.010
SMC 0.5 0.014 0.012 0.009 0.144
SMC 0.9 0.012 0.012 0.009 0.059
SMC 0.99 0.011 0.010 0.007 0.180
Metro 0.0 0.618 0.011 0.007 89.690
Metro 0.3 0.604 0.012 0.009 66.269
Metro 0.5 0.621 0.012 0.009 69.820
Metro 0.9 0.627 0.012 0.009 68.913
Metro 0.99 0.646 0.010 0.007 88.494
DEMetro_Z 0.0 0.421 0.011 0.007 60.493
DEMetro_Z 0.3 0.516 0.012 0.009 56.483
DEMetro_Z 0.5 0.614 0.012 0.009 69.107
DEMetro_Z 0.9 0.630 0.012 0.009 69.295
DEMetro_Z 0.99 0.622 0.010 0.007 85.207
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Trace Plots
Pooled
0.0 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.9 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
0.99 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
0.0 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.9 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
0.99 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
0.0
0.3
0.5
0.9
0.99
Chain
0.0
0.3
0.5
0.9
0.99

two_attr_dim

▼

Vary_Dimension_with_high_correlation (MvNormal, dimension, 30 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 0.600 0.552 0.217
HMC 5 1.637 0.108 0.586
HMC 10 4.059 0.000282 2.835
HMC 15 4.955 2.29e-05 4.181
HMC 30 5.182 1.16e-05 4.168
SMC 2 -2.265 0.0273 -0.560
SMC 5 -0.668 0.507 -0.155
SMC 10 0.020 0.984 0.006
SMC 15 1.624 0.111 0.597
SMC 30 0.336 0.738 0.081
Metro 2 4.688 5.47e-05 5.628
Metro 5 6.536 3.28e-07 10.550
Metro 10 7.266 5e-08 18.734
Metro 15 5.441 7.4e-06 29.523
Metro 30 8.432 2.58e-09 27.655
DEMetro_Z 2 3.515 0.00105 1.418
DEMetro_Z 5 8.058 6.92e-09 495.082
DEMetro_Z 10 20.055 1.52e-18 490.731
DEMetro_Z 15 27.851 1.76e-22 796.734
DEMetro_Z 30 44.001 4.11e-28 601.670
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -2.745 0.0103 -0.501
HMC_vs_DEMetro_Z 1 -8.060 6.89e-09 -1.471
HMC_vs_DEMetro_Z 2 -20.106 1.42e-18 -3.671
HMC_vs_DEMetro_Z 3 -27.754 1.95e-22 -5.067
HMC_vs_DEMetro_Z 4 -43.595 5.44e-28 -7.959
Metro_vs_SMC 0 5.103 1.9e-05 0.932
Metro_vs_SMC 1 6.800 1.82e-07 1.242
Metro_vs_SMC 2 7.173 6.78e-08 1.310
Metro_vs_SMC 3 5.267 1.21e-05 0.962
Metro_vs_SMC 4 8.482 2.4e-09 1.549
Metro_vs_DEMetro_Z 0 3.222 0.00313 0.588
Metro_vs_DEMetro_Z 1 -7.852 1.17e-08 -1.434
Metro_vs_DEMetro_Z 2 -19.557 3.01e-18 -3.571
Metro_vs_DEMetro_Z 3 -26.433 7.62e-22 -4.826
Metro_vs_DEMetro_Z 4 -43.664 5.2e-28 -7.972
HMC_vs_Metro 0 -4.196 0.000235 -0.766
HMC_vs_Metro 1 -5.972 1.72e-06 -1.090
HMC_vs_Metro 2 -6.296 7.09e-07 -1.149
HMC_vs_Metro 3 -4.594 7.83e-05 -0.839
HMC_vs_Metro 4 -7.255 5.47e-08 -1.325
HMC_vs_SMC 0 2.696 0.0116 0.492
HMC_vs_SMC 1 2.442 0.0209 0.446
HMC_vs_SMC 2 4.050 0.000349 0.739
HMC_vs_SMC 3 4.218 0.000221 0.770
HMC_vs_SMC 4 5.147 1.68e-05 0.940
DEMetro_Z_vs_SMC 0 5.143 1.71e-05 0.939
DEMetro_Z_vs_SMC 1 8.055 6.97e-09 1.471
DEMetro_Z_vs_SMC 2 20.084 1.46e-18 3.667
DEMetro_Z_vs_SMC 3 27.902 1.68e-22 5.094
DEMetro_Z_vs_SMC 4 44.004 4.17e-28 8.034
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.024 0.022 0.012 0.217
HMC 5 0.023 0.017 0.011 0.586
HMC 10 0.053 0.020 0.012 2.835
HMC 15 0.049 0.016 0.008 4.181
HMC 30 0.064 0.018 0.011 4.168
SMC 2 0.015 0.022 0.012 -0.560
SMC 5 0.015 0.017 0.011 -0.155
SMC 10 0.020 0.020 0.012 0.006
SMC 15 0.020 0.016 0.008 0.597
SMC 30 0.019 0.018 0.011 0.081
Metro 2 0.088 0.022 0.012 5.628
Metro 5 0.136 0.017 0.011 10.550
Metro 10 0.238 0.020 0.012 18.734
Metro 15 0.250 0.016 0.008 29.523
Metro 30 0.325 0.018 0.011 27.655
DEMetro_Z 2 0.038 0.022 0.012 1.418
DEMetro_Z 5 5.622 0.017 0.011 495.082
DEMetro_Z 10 5.724 0.020 0.012 490.731
DEMetro_Z 15 6.342 0.016 0.008 796.734
DEMetro_Z 30 6.702 0.018 0.011 601.670
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 3.754 0.000655 2.461
HMC 5 2.716 0.00898 0.870
HMC 10 4.364 9.92e-05 2.289
HMC 15 3.645 0.000818 1.905
HMC 30 4.719 4.66e-05 4.302
SMC 2 2.758 0.00844 1.078
SMC 5 -0.332 0.741 -0.074
SMC 10 1.082 0.284 0.333
SMC 15 -0.327 0.745 -0.089
SMC 30 -0.168 0.867 -0.044
Metro 2 6.092 9.4e-07 6.048
Metro 5 7.018 6.54e-08 6.394
Metro 10 5.958 1.72e-06 16.191
Metro 15 8.480 2.01e-09 14.500
Metro 30 5.366 9.04e-06 19.652
DEMetro_Z 2 4.772 2.98e-05 2.601
DEMetro_Z 5 5.839 2.48e-06 5538.286
DEMetro_Z 10 14.127 1.56e-14 10274.260
DEMetro_Z 15 21.758 1.65e-19 10114.031
DEMetro_Z 30 38.977 1.33e-26 12761.003
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 1.734 0.0936 0.317
HMC_vs_SMC 1 2.924 0.00665 0.534
HMC_vs_SMC 2 3.031 0.00508 0.553
HMC_vs_SMC 3 3.691 0.000919 0.674
HMC_vs_SMC 4 4.806 4.34e-05 0.878
Metro_vs_DEMetro_Z 0 3.317 0.00246 0.606
Metro_vs_DEMetro_Z 1 -5.832 2.53e-06 -1.065
Metro_vs_DEMetro_Z 2 -14.101 1.64e-14 -2.574
Metro_vs_DEMetro_Z 3 -21.721 1.73e-19 -3.966
Metro_vs_DEMetro_Z 4 -38.961 1.34e-26 -7.113
HMC_vs_Metro 0 -3.647 0.00103 -0.666
HMC_vs_Metro 1 -5.818 2.63e-06 -1.062
HMC_vs_Metro 2 -5.181 1.53e-05 -0.946
HMC_vs_Metro 3 -6.960 1.19e-07 -1.271
HMC_vs_Metro 4 -4.578 8.18e-05 -0.836
HMC_vs_DEMetro_Z 0 -0.152 0.88 -0.028
HMC_vs_DEMetro_Z 1 -5.838 2.48e-06 -1.066
HMC_vs_DEMetro_Z 2 -14.123 1.57e-14 -2.579
HMC_vs_DEMetro_Z 3 -21.762 1.65e-19 -3.973
HMC_vs_DEMetro_Z 4 -38.986 1.32e-26 -7.118
Metro_vs_SMC 0 4.992 2.59e-05 0.911
Metro_vs_SMC 1 7.271 5.23e-08 1.328
Metro_vs_SMC 2 5.841 2.46e-06 1.066
Metro_vs_SMC 3 8.450 2.6e-09 1.543
Metro_vs_SMC 4 5.387 8.66e-06 0.984
DEMetro_Z_vs_SMC 0 2.798 0.00905 0.511
DEMetro_Z_vs_SMC 1 5.839 2.48e-06 1.066
DEMetro_Z_vs_SMC 2 14.127 1.56e-14 2.579
DEMetro_Z_vs_SMC 3 21.759 1.65e-19 3.973
DEMetro_Z_vs_SMC 4 38.979 1.33e-26 7.117
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.047 0.020 0.011 2.461
HMC 5 0.050 0.031 0.022 0.870
HMC 10 0.056 0.026 0.013 2.289
HMC 15 0.061 0.031 0.016 1.905
HMC 30 0.090 0.029 0.014 4.302
SMC 2 0.032 0.020 0.011 1.078
SMC 5 0.029 0.031 0.022 -0.074
SMC 10 0.031 0.026 0.013 0.333
SMC 15 0.029 0.031 0.016 -0.089
SMC 30 0.029 0.029 0.014 -0.044
Metro 2 0.087 0.020 0.011 6.048
Metro 5 0.173 0.031 0.022 6.394
Metro 10 0.232 0.026 0.013 16.191
Metro 15 0.261 0.031 0.016 14.500
Metro 30 0.307 0.029 0.014 19.652
DEMetro_Z 2 0.049 0.020 0.011 2.601
DEMetro_Z 5 123.310 0.031 0.022 5538.286
DEMetro_Z 10 130.393 0.026 0.013 10274.260
DEMetro_Z 15 160.845 0.031 0.016 10114.031
DEMetro_Z 30 180.332 0.029 0.014 12761.003
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 2.462 0.018 1.022
HMC 5 3.500 0.00112 1.456
HMC 10 5.416 5.74e-06 4.246
HMC 15 6.766 1.49e-07 7.308
HMC 30 7.100 5.37e-08 6.693
SMC 2 -1.612 0.112 -0.423
SMC 5 -0.640 0.525 -0.143
SMC 10 0.564 0.575 0.150
SMC 15 1.807 0.0777 0.721
SMC 30 0.166 0.869 0.038
Metro 2 6.004 1.37e-06 8.157
Metro 5 9.942 5.74e-11 16.092
Metro 10 9.749 1.09e-10 29.661
Metro 15 6.971 1.15e-07 50.079
Metro 30 11.431 2.73e-12 41.283
DEMetro_Z 2 5.793 9.73e-07 2.677
DEMetro_Z 5 13.240 8.02e-14 1098.317
DEMetro_Z 10 28.428 9.95e-23 1292.195
DEMetro_Z 15 44.986 2.22e-28 2401.913
DEMetro_Z 30 85.928 1.79e-36 1581.502
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 3.777 0.000731 0.690
Metro_vs_DEMetro_Z 1 -12.995 1.28e-13 -2.372
Metro_vs_DEMetro_Z 2 -28.048 1.45e-22 -5.121
Metro_vs_DEMetro_Z 3 -44.511 3e-28 -8.127
Metro_vs_DEMetro_Z 4 -87.683 1.01e-36 -16.009
DEMetro_Z_vs_SMC 0 7.161 7e-08 1.307
DEMetro_Z_vs_SMC 1 13.239 8.03e-14 2.417
DEMetro_Z_vs_SMC 2 28.404 1.02e-22 5.186
DEMetro_Z_vs_SMC 3 45.022 2.17e-28 8.220
DEMetro_Z_vs_SMC 4 85.902 1.83e-36 15.684
HMC_vs_DEMetro_Z 0 -2.830 0.00837 -0.517
HMC_vs_DEMetro_Z 1 -13.235 8.09e-14 -2.416
HMC_vs_DEMetro_Z 2 -28.510 9.19e-23 -5.205
HMC_vs_DEMetro_Z 3 -44.970 2.24e-28 -8.210
HMC_vs_DEMetro_Z 4 -84.918 2.55e-36 -15.504
HMC_vs_Metro 0 -4.800 4.43e-05 -0.876
HMC_vs_Metro 1 -8.443 2.64e-09 -1.542
HMC_vs_Metro 2 -8.863 9.48e-10 -1.618
HMC_vs_Metro 3 -5.950 1.83e-06 -1.086
HMC_vs_Metro 4 -10.144 4.77e-11 -1.852
HMC_vs_SMC 0 4.228 0.000215 0.772
HMC_vs_SMC 1 4.132 0.000279 0.754
HMC_vs_SMC 2 5.286 1.15e-05 0.965
HMC_vs_SMC 3 6.057 1.36e-06 1.106
HMC_vs_SMC 4 6.915 1.34e-07 1.263
Metro_vs_SMC 0 6.198 9.27e-07 1.132
Metro_vs_SMC 1 10.301 3.36e-11 1.881
Metro_vs_SMC 2 9.612 1.61e-10 1.755
Metro_vs_SMC 3 6.805 1.8e-07 1.242
Metro_vs_SMC 4 11.403 3.1e-12 2.082
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.036 0.028 0.008 1.022
HMC 5 0.035 0.024 0.007 1.456
HMC 10 0.054 0.025 0.007 4.246
HMC 15 0.053 0.023 0.004 7.308
HMC 30 0.070 0.025 0.007 6.693
SMC 2 0.025 0.028 0.008 -0.423
SMC 5 0.023 0.024 0.007 -0.143
SMC 10 0.026 0.025 0.007 0.150
SMC 15 0.026 0.023 0.004 0.721
SMC 30 0.025 0.025 0.007 0.038
Metro 2 0.091 0.028 0.008 8.157
Metro 5 0.143 0.024 0.007 16.092
Metro 10 0.227 0.025 0.007 29.661
Metro 15 0.230 0.023 0.004 50.079
Metro 30 0.302 0.025 0.007 41.283
DEMetro_Z 2 0.049 0.028 0.008 2.677
DEMetro_Z 5 8.170 0.024 0.007 1098.317
DEMetro_Z 10 8.837 0.025 0.007 1292.195
DEMetro_Z 15 9.964 0.023 0.004 2401.913
DEMetro_Z 30 10.643 0.025 0.007 1581.502
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 1.944 0.0585 0.795
HMC 5 3.270 0.00191 1.040
HMC 10 6.009 9.39e-07 4.308
HMC 15 6.560 2.12e-07 5.271
HMC 30 7.261 2.69e-08 5.489
SMC 2 -1.574 0.121 -0.412
SMC 5 -1.080 0.285 -0.242
SMC 10 1.312 0.195 0.384
SMC 15 0.969 0.337 0.339
SMC 30 -0.460 0.647 -0.101
Metro 2 5.802 2.37e-06 7.393
Metro 5 11.968 3.73e-13 11.965
Metro 10 12.553 2.41e-13 26.745
Metro 15 8.360 3.18e-09 40.117
Metro 30 11.436 2.55e-12 30.635
DEMetro_Z 2 4.490 5.62e-05 1.925
DEMetro_Z 5 42.304 8.25e-28 111.762
DEMetro_Z 10 61.896 1.1e-32 139.765
DEMetro_Z 15 59.948 3.78e-32 175.702
DEMetro_Z 30 118.412 4.76e-44 94.855
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 6.175 9.86e-07 1.127
DEMetro_Z_vs_SMC 1 42.301 1.29e-27 7.723
DEMetro_Z_vs_SMC 2 61.138 3.32e-32 11.162
DEMetro_Z_vs_SMC 3 59.097 8.83e-32 10.790
DEMetro_Z_vs_SMC 4 122.191 6.85e-41 22.309
HMC_vs_Metro 0 -4.824 4.14e-05 -0.881
HMC_vs_Metro 1 -10.483 2.24e-11 -1.914
HMC_vs_Metro 2 -10.505 2.13e-11 -1.918
HMC_vs_Metro 3 -7.129 7.62e-08 -1.301
HMC_vs_Metro 4 -9.919 7.93e-11 -1.811
Metro_vs_DEMetro_Z 0 4.216 0.000222 0.770
Metro_vs_DEMetro_Z 1 -35.381 2.08e-25 -6.460
Metro_vs_DEMetro_Z 2 -39.687 7.94e-27 -7.246
Metro_vs_DEMetro_Z 3 -23.832 1.35e-20 -4.351
Metro_vs_DEMetro_Z 4 -24.521 6.14e-21 -4.477
HMC_vs_SMC 0 2.960 0.00607 0.540
HMC_vs_SMC 1 4.322 0.000166 0.789
HMC_vs_SMC 2 5.404 8.26e-06 0.987
HMC_vs_SMC 3 6.080 1.28e-06 1.110
HMC_vs_SMC 4 7.148 7.24e-08 1.305
Metro_vs_SMC 0 6.117 1.16e-06 1.117
Metro_vs_SMC 1 12.543 3.07e-13 2.290
Metro_vs_SMC 2 12.224 5.77e-13 2.232
Metro_vs_SMC 3 8.191 4.96e-09 1.495
Metro_vs_SMC 4 11.430 2.92e-12 2.087
HMC_vs_DEMetro_Z 0 -1.973 0.0581 -0.360
HMC_vs_DEMetro_Z 1 -42.578 1.07e-27 -7.774
HMC_vs_DEMetro_Z 2 -55.435 5.56e-31 -10.121
HMC_vs_DEMetro_Z 3 -55.813 4.57e-31 -10.190
HMC_vs_DEMetro_Z 4 -86.901 1.31e-36 -15.866
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.018 0.014 0.005 0.795
HMC 5 0.020 0.014 0.006 1.040
HMC 10 0.032 0.014 0.004 4.308
HMC 15 0.032 0.014 0.003 5.271
HMC 30 0.047 0.015 0.006 5.489
SMC 2 0.012 0.014 0.005 -0.412
SMC 5 0.012 0.014 0.006 -0.242
SMC 10 0.015 0.014 0.004 0.384
SMC 15 0.015 0.014 0.003 0.339
SMC 30 0.014 0.015 0.006 -0.101
Metro 2 0.049 0.014 0.005 7.393
Metro 5 0.089 0.014 0.006 11.965
Metro 10 0.131 0.014 0.004 26.745
Metro 15 0.150 0.014 0.003 40.117
Metro 30 0.193 0.015 0.006 30.635
DEMetro_Z 2 0.023 0.014 0.005 1.925
DEMetro_Z 5 0.712 0.014 0.006 111.762
DEMetro_Z 10 0.625 0.014 0.004 139.765
DEMetro_Z 15 0.609 0.014 0.003 175.702
DEMetro_Z 30 0.566 0.015 0.006 94.855
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 1.719 0.093 0.709
HMC 5 3.531 0.000994 1.401
HMC 10 3.393 0.00157 1.540
HMC 15 6.289 4.95e-07 5.501
HMC 30 4.738 4.45e-05 4.444
SMC 2 -1.193 0.238 -0.308
SMC 5 -0.353 0.725 -0.084
SMC 10 -0.840 0.404 -0.215
SMC 15 2.150 0.0366 0.741
SMC 30 -0.048 0.962 -0.011
Metro 2 5.167 1.38e-05 5.781
Metro 5 7.273 4.38e-08 11.049
Metro 10 6.922 1.23e-07 15.907
Metro 15 6.248 8.01e-07 33.356
Metro 30 6.802 1.79e-07 32.981
DEMetro_Z 2 2.830 0.00712 1.188
DEMetro_Z 5 4.847 3.88e-05 360.695
DEMetro_Z 10 14.938 3.74e-15 902.143
DEMetro_Z 15 17.641 4.78e-17 1355.747
DEMetro_Z 30 43.404 6.14e-28 1034.567
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -0.864 0.395 -0.158
HMC_vs_DEMetro_Z 1 -4.821 4.17e-05 -0.880
HMC_vs_DEMetro_Z 2 -14.938 3.74e-15 -2.727
HMC_vs_DEMetro_Z 3 -17.523 5.71e-17 -3.199
HMC_vs_DEMetro_Z 4 -43.197 7.07e-28 -7.887
Metro_vs_SMC 0 5.307 1.08e-05 0.969
Metro_vs_SMC 1 7.576 2.37e-08 1.383
Metro_vs_SMC 2 6.987 1.11e-07 1.276
Metro_vs_SMC 3 6.035 1.45e-06 1.102
Metro_vs_SMC 4 6.743 2.12e-07 1.231
Metro_vs_DEMetro_Z 0 4.227 0.000215 0.772
Metro_vs_DEMetro_Z 1 -4.693 5.94e-05 -0.857
Metro_vs_DEMetro_Z 2 -14.694 5.71e-15 -2.683
Metro_vs_DEMetro_Z 3 -17.244 8.75e-17 -3.148
Metro_vs_DEMetro_Z 4 -42.338 1.26e-27 -7.730
HMC_vs_Metro 0 -4.737 5.27e-05 -0.865
HMC_vs_Metro 1 -6.294 7.13e-07 -1.149
HMC_vs_Metro 2 -6.039 1.43e-06 -1.103
HMC_vs_Metro 3 -5.154 1.65e-05 -0.941
HMC_vs_Metro 4 -5.372 9.01e-06 -0.981
HMC_vs_SMC 0 2.448 0.0207 0.447
HMC_vs_SMC 1 3.913 0.000506 0.714
HMC_vs_SMC 2 3.732 0.000823 0.681
HMC_vs_SMC 3 5.140 1.72e-05 0.938
HMC_vs_SMC 4 4.793 4.5e-05 0.875
DEMetro_Z_vs_SMC 0 3.711 0.000872 0.678
DEMetro_Z_vs_SMC 1 4.846 3.89e-05 0.885
DEMetro_Z_vs_SMC 2 14.942 3.71e-15 2.728
DEMetro_Z_vs_SMC 3 17.630 4.86e-17 3.219
DEMetro_Z_vs_SMC 4 43.377 6.28e-28 7.919
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.030 0.022 0.012 0.709
HMC 5 0.032 0.017 0.011 1.401
HMC 10 0.038 0.020 0.012 1.540
HMC 15 0.059 0.016 0.008 5.501
HMC 30 0.068 0.018 0.011 4.444
SMC 2 0.018 0.022 0.012 -0.308
SMC 5 0.016 0.017 0.011 -0.084
SMC 10 0.018 0.020 0.012 -0.215
SMC 15 0.021 0.016 0.008 0.741
SMC 30 0.018 0.018 0.011 -0.011
Metro 2 0.089 0.022 0.012 5.781
Metro 5 0.142 0.017 0.011 11.049
Metro 10 0.205 0.020 0.012 15.907
Metro 15 0.280 0.016 0.008 33.356
Metro 30 0.385 0.018 0.011 32.981
DEMetro_Z 2 0.036 0.022 0.012 1.188
DEMetro_Z 5 4.100 0.017 0.011 360.695
DEMetro_Z 10 10.506 0.020 0.012 902.143
DEMetro_Z 15 10.780 0.016 0.008 1355.747
DEMetro_Z 30 11.512 0.018 0.011 1034.567
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 3.324 0.00171 1.172
HMC 5 2.711 0.00901 0.833
HMC 10 2.907 0.00641 1.935
HMC 15 3.428 0.00157 2.023
HMC 30 4.978 2.39e-05 5.804
SMC 2 2.197 0.0334 0.870
SMC 5 -0.587 0.56 -0.130
SMC 10 0.276 0.783 0.078
SMC 15 -0.806 0.424 -0.195
SMC 30 -0.764 0.448 -0.195
Metro 2 6.499 2.2e-07 4.593
Metro 5 4.934 2.52e-05 4.540
Metro 10 7.318 4.21e-08 14.961
Metro 15 5.265 1.16e-05 11.262
Metro 30 11.361 2.95e-12 28.858
DEMetro_Z 2 5.450 3.53e-06 2.863
DEMetro_Z 5 3.756 0.000773 993.211
DEMetro_Z 10 5.948 1.84e-06 1906.429
DEMetro_Z 15 9.478 2.2e-10 1198.219
DEMetro_Z 30 14.515 7.81e-15 1337.020
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 0.603 0.551 0.110
HMC_vs_SMC 1 3.547 0.00135 0.648
HMC_vs_SMC 2 2.614 0.014 0.477
HMC_vs_SMC 3 3.711 0.000872 0.678
HMC_vs_SMC 4 5.205 1.43e-05 0.950
Metro_vs_DEMetro_Z 0 2.060 0.0485 0.376
Metro_vs_DEMetro_Z 1 -3.739 0.000809 -0.683
Metro_vs_DEMetro_Z 2 -5.904 2.07e-06 -1.078
Metro_vs_DEMetro_Z 3 -9.392 2.68e-10 -1.715
Metro_vs_DEMetro_Z 4 -14.190 1.39e-14 -2.591
HMC_vs_Metro 0 -5.065 2.12e-05 -0.925
HMC_vs_Metro 1 -3.843 0.000611 -0.702
HMC_vs_Metro 2 -6.199 9.24e-07 -1.132
HMC_vs_Metro 3 -4.202 0.00023 -0.767
HMC_vs_Metro 4 -8.395 2.98e-09 -1.533
HMC_vs_DEMetro_Z 0 -2.673 0.0122 -0.488
HMC_vs_DEMetro_Z 1 -3.752 0.000781 -0.685
HMC_vs_DEMetro_Z 2 -5.940 1.88e-06 -1.085
HMC_vs_DEMetro_Z 3 -9.473 2.22e-10 -1.730
HMC_vs_DEMetro_Z 4 -14.448 8.81e-15 -2.638
Metro_vs_SMC 0 4.565 8.49e-05 0.833
Metro_vs_SMC 1 5.287 1.14e-05 0.965
Metro_vs_SMC 2 7.136 7.47e-08 1.303
Metro_vs_SMC 3 5.346 9.7e-06 0.976
Metro_vs_SMC 4 11.370 3.32e-12 2.076
DEMetro_Z_vs_SMC 0 3.805 0.000677 0.695
DEMetro_Z_vs_SMC 1 3.756 0.000773 0.686
DEMetro_Z_vs_SMC 2 5.949 1.83e-06 1.086
DEMetro_Z_vs_SMC 3 9.479 2.19e-10 1.731
DEMetro_Z_vs_SMC 4 14.525 7.69e-15 2.652
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.033 0.020 0.011 1.172
HMC 5 0.050 0.031 0.022 0.833
HMC 10 0.051 0.026 0.013 1.935
HMC 15 0.063 0.031 0.016 2.023
HMC 30 0.111 0.029 0.014 5.804
SMC 2 0.030 0.020 0.011 0.870
SMC 5 0.028 0.031 0.022 -0.130
SMC 10 0.027 0.026 0.013 0.078
SMC 15 0.028 0.031 0.016 -0.195
SMC 30 0.027 0.029 0.014 -0.195
Metro 2 0.071 0.020 0.011 4.593
Metro 5 0.132 0.031 0.022 4.540
Metro 10 0.216 0.026 0.013 14.961
Metro 15 0.210 0.031 0.016 11.262
Metro 30 0.437 0.029 0.014 28.858
DEMetro_Z 2 0.052 0.020 0.011 2.863
DEMetro_Z 5 22.139 0.031 0.022 993.211
DEMetro_Z 10 24.216 0.026 0.013 1906.429
DEMetro_Z 15 19.082 0.031 0.016 1198.219
DEMetro_Z 30 18.920 0.029 0.014 1337.020
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 2.393 0.0212 1.000
HMC 5 5.147 5.7e-06 1.967
HMC 10 5.978 6.2e-07 2.972
HMC 15 8.784 6.97e-10 9.461
HMC 30 6.699 1.83e-07 7.547
SMC 2 -0.156 0.877 -0.039
SMC 5 0.167 0.868 0.042
SMC 10 -0.271 0.788 -0.067
SMC 15 2.485 0.0168 0.967
SMC 30 -0.964 0.34 -0.218
Metro 2 6.355 5.11e-07 8.490
Metro 5 8.851 8e-10 15.225
Metro 10 8.594 1.71e-09 24.772
Metro 15 7.295 4.88e-08 54.532
Metro 30 9.668 1.38e-10 52.166
DEMetro_Z 2 6.600 5.52e-08 2.768
DEMetro_Z 5 5.304 1.09e-05 481.155
DEMetro_Z 10 14.662 6.04e-15 1347.942
DEMetro_Z 15 18.202 2.07e-17 2195.599
DEMetro_Z 30 41.433 2.32e-27 1422.451
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 4.413 0.000129 0.806
Metro_vs_DEMetro_Z 1 -5.135 1.74e-05 -0.938
Metro_vs_DEMetro_Z 2 -14.408 9.45e-15 -2.631
Metro_vs_DEMetro_Z 3 -17.782 3.87e-17 -3.247
Metro_vs_DEMetro_Z 4 -39.800 7.32e-27 -7.267
DEMetro_Z_vs_SMC 0 7.078 8.7e-08 1.292
DEMetro_Z_vs_SMC 1 5.302 1.1e-05 0.968
DEMetro_Z_vs_SMC 2 14.662 6.04e-15 2.677
DEMetro_Z_vs_SMC 3 18.191 2.11e-17 3.321
DEMetro_Z_vs_SMC 4 41.463 2.28e-27 7.570
HMC_vs_DEMetro_Z 0 -3.611 0.00114 -0.659
HMC_vs_DEMetro_Z 1 -5.276 1.18e-05 -0.963
HMC_vs_DEMetro_Z 2 -14.644 6.24e-15 -2.674
HMC_vs_DEMetro_Z 3 -18.099 2.42e-17 -3.304
HMC_vs_DEMetro_Z 4 -41.218 2.7e-27 -7.525
HMC_vs_Metro 0 -5.773 2.97e-06 -1.054
HMC_vs_Metro 1 -7.878 1.09e-08 -1.438
HMC_vs_Metro 2 -7.107 8.06e-08 -1.298
HMC_vs_Metro 3 -5.946 1.85e-06 -1.086
HMC_vs_Metro 4 -7.570 2.4e-08 -1.382
HMC_vs_SMC 0 2.579 0.0153 0.471
HMC_vs_SMC 1 5.112 1.86e-05 0.933
HMC_vs_SMC 2 5.582 5.04e-06 1.019
HMC_vs_SMC 3 7.910 1.01e-08 1.444
HMC_vs_SMC 4 6.832 1.67e-07 1.247
Metro_vs_SMC 0 6.328 6.5e-07 1.155
Metro_vs_SMC 1 8.854 9.68e-10 1.616
Metro_vs_SMC 2 8.667 1.52e-09 1.582
Metro_vs_SMC 3 7.142 7.36e-08 1.304
Metro_vs_SMC 4 9.637 1.52e-10 1.759
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.036 0.028 0.008 1.000
HMC 5 0.039 0.024 0.007 1.967
HMC 10 0.045 0.025 0.007 2.972
HMC 15 0.062 0.023 0.004 9.461
HMC 30 0.076 0.025 0.007 7.547
SMC 2 0.028 0.028 0.008 -0.039
SMC 5 0.024 0.024 0.007 0.042
SMC 10 0.025 0.025 0.007 -0.067
SMC 15 0.027 0.023 0.004 0.967
SMC 30 0.023 0.025 0.007 -0.218
Metro 2 0.093 0.028 0.008 8.490
Metro 5 0.137 0.024 0.007 15.225
Metro 10 0.194 0.025 0.007 24.772
Metro 15 0.249 0.023 0.004 54.532
Metro 30 0.375 0.025 0.007 52.166
DEMetro_Z 2 0.049 0.028 0.008 2.768
DEMetro_Z 5 3.593 0.024 0.007 481.155
DEMetro_Z 10 9.217 0.025 0.007 1347.942
DEMetro_Z 15 9.110 0.023 0.004 2195.599
DEMetro_Z 30 9.575 0.025 0.007 1422.451
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 2.367 0.0225 0.947
HMC 5 4.747 1.47e-05 1.361
HMC 10 6.393 1.77e-07 3.256
HMC 15 8.825 3.73e-10 6.644
HMC 30 6.955 6.36e-08 5.216
SMC 2 0.123 0.902 0.031
SMC 5 -0.650 0.519 -0.143
SMC 10 0.358 0.721 0.102
SMC 15 1.836 0.0726 0.642
SMC 30 -1.535 0.131 -0.324
Metro 2 7.326 3.13e-08 7.668
Metro 5 9.607 9.93e-11 11.241
Metro 10 8.921 7.63e-10 24.791
Metro 15 8.319 3.52e-09 41.637
Metro 30 11.560 2.08e-12 40.873
DEMetro_Z 2 6.481 5.37e-08 2.377
DEMetro_Z 5 10.818 1.06e-11 80.378
DEMetro_Z 10 40.183 5.01e-27 212.181
DEMetro_Z 15 75.036 6.69e-35 277.792
DEMetro_Z 30 63.518 6.08e-33 161.317
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 7.225 5.9e-08 1.319
DEMetro_Z_vs_SMC 1 10.808 1.1e-11 1.973
DEMetro_Z_vs_SMC 2 39.918 6.73e-27 7.288
DEMetro_Z_vs_SMC 3 74.724 1.02e-34 13.643
DEMetro_Z_vs_SMC 4 63.878 9.41e-33 11.663
HMC_vs_Metro 0 -6.931 1.28e-07 -1.265
HMC_vs_Metro 1 -9.027 6.38e-10 -1.648
HMC_vs_Metro 2 -7.255 5.47e-08 -1.324
HMC_vs_Metro 3 -7.063 9.06e-08 -1.289
HMC_vs_Metro 4 -9.408 2.59e-10 -1.718
Metro_vs_DEMetro_Z 0 4.981 2.67e-05 0.909
Metro_vs_DEMetro_Z 1 -9.601 1.65e-10 -1.753
Metro_vs_DEMetro_Z 2 -33.795 7.63e-25 -6.170
Metro_vs_DEMetro_Z 3 -41.455 2.29e-27 -7.569
Metro_vs_DEMetro_Z 4 -30.324 1.63e-23 -5.536
HMC_vs_SMC 0 2.503 0.0182 0.457
HMC_vs_SMC 1 5.982 1.67e-06 1.092
HMC_vs_SMC 2 5.208 1.42e-05 0.951
HMC_vs_SMC 3 8.170 5.22e-09 1.492
HMC_vs_SMC 4 7.397 3.77e-08 1.350
Metro_vs_SMC 0 7.381 3.93e-08 1.348
Metro_vs_SMC 1 9.640 1.51e-10 1.760
Metro_vs_SMC 2 8.873 9.25e-10 1.620
Metro_vs_SMC 3 8.272 4.05e-09 1.510
Metro_vs_SMC 4 11.524 2.4e-12 2.104
HMC_vs_DEMetro_Z 0 -3.385 0.00206 -0.618
HMC_vs_DEMetro_Z 1 -10.555 1.91e-11 -1.927
HMC_vs_DEMetro_Z 2 -40.139 5.75e-27 -7.328
HMC_vs_DEMetro_Z 3 -68.426 1.3e-33 -12.493
HMC_vs_DEMetro_Z 4 -55.312 5.92e-31 -10.098
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.019 0.014 0.005 0.947
HMC 5 0.022 0.014 0.006 1.361
HMC 10 0.028 0.014 0.004 3.256
HMC 15 0.036 0.014 0.003 6.644
HMC 30 0.045 0.015 0.006 5.216
SMC 2 0.015 0.014 0.005 0.031
SMC 5 0.013 0.014 0.006 -0.143
SMC 10 0.014 0.014 0.004 0.102
SMC 15 0.016 0.014 0.003 0.642
SMC 30 0.013 0.015 0.006 -0.324
Metro 2 0.050 0.014 0.005 7.668
Metro 5 0.084 0.014 0.006 11.241
Metro 10 0.122 0.014 0.004 24.791
Metro 15 0.155 0.014 0.003 41.637
Metro 30 0.253 0.015 0.006 40.873
DEMetro_Z 2 0.025 0.014 0.005 2.377
DEMetro_Z 5 0.516 0.014 0.006 80.378
DEMetro_Z 10 0.942 0.014 0.004 212.181
DEMetro_Z 15 0.954 0.014 0.003 277.792
DEMetro_Z 30 0.952 0.015 0.006 161.317
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
Trace Plots
Pooled
2 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
30 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
30 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2
5
10
15
30
Chain
2
5
10
15
30

Vary_Dimension_with_heavy_Tails (MvStudentT, dimension, 30 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 0.274 0.785 0.074
HMC 5 1.682 0.0984 0.512
HMC 10 1.495 0.146 2.917
HMC 15 1.396 0.169 0.478
HMC 30 1.440 0.161 16.644
SMC 2 3.170 0.0025 0.938
SMC 5 10.453 2.27e-11 39.706
SMC 10 19.912 1.63e-18 72.996
SMC 15 29.449 9.58e-25 24.270
SMC 30 54.838 3.99e-31 129.468
Metro 2 2.224 0.0322 1.110
Metro 5 3.406 0.0018 2.845
Metro 10 8.570 6.56e-10 6.112
Metro 15 6.137 2.65e-07 2.611
Metro 30 6.923 1.26e-07 20.035
DEMetro_Z 2 3.167 0.00282 1.272
DEMetro_Z 5 6.625 2.91e-07 150.211
DEMetro_Z 10 13.335 6.67e-14 229.867
DEMetro_Z 15 17.727 3.85e-17 74.479
DEMetro_Z 30 22.869 4.2e-20 481.992
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -2.840 0.00816 -0.519
HMC_vs_DEMetro_Z 1 -6.623 2.93e-07 -1.209
HMC_vs_DEMetro_Z 2 -13.563 4.37e-14 -2.476
HMC_vs_DEMetro_Z 3 -17.420 6.68e-17 -3.180
HMC_vs_DEMetro_Z 4 -19.616 2.77e-18 -3.581
Metro_vs_SMC 0 0.345 0.733 0.063
Metro_vs_SMC 1 -9.745 1.18e-10 -1.779
Metro_vs_SMC 2 -17.302 8.01e-17 -3.159
Metro_vs_SMC 3 -28.711 7.54e-23 -5.242
Metro_vs_SMC 4 -27.598 2.28e-22 -5.039
Metro_vs_DEMetro_Z 0 -0.253 0.802 -0.046
Metro_vs_DEMetro_Z 1 -6.486 4.24e-07 -1.184
Metro_vs_DEMetro_Z 2 -13.144 9.61e-14 -2.400
Metro_vs_DEMetro_Z 3 -16.922 1.44e-16 -3.090
Metro_vs_DEMetro_Z 4 -21.929 1.33e-19 -4.004
HMC_vs_Metro 0 -1.925 0.064 -0.352
HMC_vs_Metro 1 -2.700 0.0115 -0.493
HMC_vs_Metro 2 -1.578 0.126 -0.288
HMC_vs_Metro 3 -6.203 9.15e-07 -1.132
HMC_vs_Metro 4 -0.273 0.787 -0.050
HMC_vs_SMC 0 -4.037 0.000362 -0.737
HMC_vs_SMC 1 -10.314 3.26e-11 -1.883
HMC_vs_SMC 2 -16.135 5.05e-16 -2.946
HMC_vs_SMC 3 -28.587 8.52e-23 -5.219
HMC_vs_SMC 4 -9.532 1.93e-10 -1.740
DEMetro_Z_vs_SMC 0 0.764 0.451 0.140
DEMetro_Z_vs_SMC 1 4.636 6.96e-05 0.846
DEMetro_Z_vs_SMC 2 8.686 1.46e-09 1.586
DEMetro_Z_vs_SMC 3 11.903 1.1e-12 2.173
DEMetro_Z_vs_SMC 4 16.166 4.8e-16 2.952
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.068 0.065 0.042 0.074
HMC 5 0.074 0.064 0.020 0.512
HMC 10 0.104 0.061 0.015 2.917
HMC 15 0.099 0.073 0.054 0.478
HMC 30 0.327 0.064 0.016 16.644
SMC 2 0.104 0.065 0.042 0.938
SMC 5 0.865 0.064 0.020 39.706
SMC 10 1.143 0.061 0.015 72.996
SMC 15 1.381 0.073 0.054 24.270
SMC 30 2.110 0.064 0.016 129.468
Metro 2 0.111 0.065 0.042 1.110
Metro 5 0.121 0.064 0.020 2.845
Metro 10 0.152 0.061 0.015 6.112
Metro 15 0.214 0.073 0.054 2.611
Metro 30 0.381 0.064 0.016 20.035
DEMetro_Z 2 0.118 0.065 0.042 1.272
DEMetro_Z 5 3.097 0.064 0.020 150.211
DEMetro_Z 10 3.469 0.061 0.015 229.867
DEMetro_Z 15 4.088 0.073 0.054 74.479
DEMetro_Z 30 7.680 0.064 0.016 481.992
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 -1.263 0.213 -0.261
HMC 5 -1.272 0.209 -0.301
HMC 10 0.382 0.704 0.129
HMC 15 -1.057 0.299 -0.193
HMC 30 1.075 0.291 368.475
SMC 2 1.444 0.155 0.306
SMC 5 37.872 1.97e-26 98.791
SMC 10 77.673 2.66e-35 333.745
SMC 15 62.168 2.42e-54 16.958
SMC 30 216.976 2.37e-48 732.009
Metro 2 -1.559 0.127 -0.308
Metro 5 -1.566 0.124 -0.327
Metro 10 -0.446 0.657 -0.099
Metro 15 -0.749 0.459 -0.138
Metro 30 3.096 0.00431 12.511
DEMetro_Z 2 -1.544 0.132 -0.294
DEMetro_Z 5 4.989 2.61e-05 61.426
DEMetro_Z 10 8.231 4.46e-09 88.169
DEMetro_Z 15 8.211 3.15e-10 3.497
DEMetro_Z 30 17.668 4.54e-17 204.927
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -3.550 0.00134 -0.648
HMC_vs_SMC 1 -38.572 1.79e-26 -7.042
HMC_vs_SMC 2 -76.849 4.55e-35 -14.031
HMC_vs_SMC 3 -84.772 2.68e-36 -15.477
HMC_vs_SMC 4 -1.060 0.298 -0.194
Metro_vs_DEMetro_Z 0 -0.235 0.816 -0.043
Metro_vs_DEMetro_Z 1 -5.028 2.34e-05 -0.918
Metro_vs_DEMetro_Z 2 -8.240 4.39e-09 -1.504
Metro_vs_DEMetro_Z 3 -9.522 1.98e-10 -1.738
Metro_vs_DEMetro_Z 4 -14.624 6.45e-15 -2.670
HMC_vs_Metro 0 0.458 0.651 0.084
HMC_vs_Metro 1 0.199 0.844 0.036
HMC_vs_Metro 2 0.809 0.425 0.148
HMC_vs_Metro 3 -2.661 0.0126 -0.486
HMC_vs_Metro 4 1.037 0.308 0.189
HMC_vs_DEMetro_Z 0 0.398 0.693 0.073
HMC_vs_DEMetro_Z 1 -5.019 2.41e-05 -0.916
HMC_vs_DEMetro_Z 2 -8.242 4.37e-09 -1.505
HMC_vs_DEMetro_Z 3 -9.605 1.63e-10 -1.754
HMC_vs_DEMetro_Z 4 0.476 0.638 0.087
Metro_vs_SMC 0 -4.340 0.000158 -0.792
Metro_vs_SMC 1 -38.459 1.94e-26 -7.022
Metro_vs_SMC 2 -77.617 3.42e-35 -14.171
Metro_vs_SMC 3 -85.123 2.38e-36 -15.541
Metro_vs_SMC 4 -115.954 3.12e-40 -21.170
DEMetro_Z_vs_SMC 0 -4.653 6.65e-05 -0.849
DEMetro_Z_vs_SMC 1 -3.056 0.00479 -0.558
DEMetro_Z_vs_SMC 2 -19.357 3.97e-18 -3.534
DEMetro_Z_vs_SMC 3 -30.983 8.87e-24 -5.657
DEMetro_Z_vs_SMC 4 -44.721 2.62e-28 -8.165
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 5.393 9.112 14.240 -0.261
HMC 5 5.929 8.258 7.752 -0.301
HMC 10 6.646 5.887 5.869 0.129
HMC 15 5.482 33.673 146.019 -0.193
HMC 30 1517.615 5.303 4.104 368.475
SMC 2 13.466 9.112 14.240 0.306
SMC 5 774.082 8.258 7.752 98.791
SMC 10 1964.573 5.887 5.869 333.745
SMC 15 2509.819 33.673 146.019 16.958
SMC 30 3009.650 5.303 4.104 732.009
Metro 2 4.722 9.112 14.240 -0.308
Metro 5 5.721 8.258 7.752 -0.327
Metro 10 5.308 5.887 5.869 -0.099
Metro 15 13.538 33.673 146.019 -0.138
Metro 30 56.650 5.303 4.104 12.511
DEMetro_Z 2 4.919 9.112 14.240 -0.294
DEMetro_Z 5 484.431 8.258 7.752 61.426
DEMetro_Z 10 523.337 5.887 5.869 88.169
DEMetro_Z 15 544.313 33.673 146.019 3.497
DEMetro_Z 30 846.376 5.303 4.104 204.927
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 1.728 0.0896 0.504
HMC 5 3.708 0.00068 1.918
HMC 10 2.074 0.047 9.677
HMC 15 3.911 0.000441 3.006
HMC 30 1.546 0.133 111.810
SMC 2 11.540 1.65e-12 18.687
SMC 5 58.057 1.44e-31 797.447
SMC 10 135.774 3.16e-42 1946.292
SMC 15 156.557 4.06e-44 735.400
SMC 30 411.661 2.82e-56 2362.188
Metro 2 5.809 1.02e-06 2.831
Metro 5 6.677 1.52e-07 5.386
Metro 10 9.721 7.7e-11 11.596
Metro 15 4.962 2.73e-05 11.545
Metro 30 7.245 5.59e-08 101.214
DEMetro_Z 2 9.384 1.13e-11 4.196
DEMetro_Z 5 7.398 3.76e-08 347.088
DEMetro_Z 10 17.014 1.25e-16 736.254
DEMetro_Z 15 18.692 1.01e-17 286.270
DEMetro_Z 30 35.280 2.25e-25 1159.241
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -2.450 0.0205 -0.447
Metro_vs_DEMetro_Z 1 -7.298 4.88e-08 -1.332
Metro_vs_DEMetro_Z 2 -16.895 1.5e-16 -3.085
Metro_vs_DEMetro_Z 3 -18.277 1.86e-17 -3.337
Metro_vs_DEMetro_Z 4 -28.069 1.42e-22 -5.125
DEMetro_Z_vs_SMC 0 -8.498 2.31e-09 -1.552
DEMetro_Z_vs_SMC 1 -9.863 9.02e-11 -1.801
DEMetro_Z_vs_SMC 2 -24.675 5.16e-21 -4.505
DEMetro_Z_vs_SMC 3 -27.013 4.15e-22 -4.932
DEMetro_Z_vs_SMC 4 -36.723 7.23e-26 -6.705
HMC_vs_DEMetro_Z 0 -9.243 3.82e-10 -1.687
HMC_vs_DEMetro_Z 1 -7.362 4.13e-08 -1.344
HMC_vs_DEMetro_Z 2 -17.307 7.94e-17 -3.160
HMC_vs_DEMetro_Z 3 -18.490 1.36e-17 -3.376
HMC_vs_DEMetro_Z 4 -13.574 4.29e-14 -2.478
HMC_vs_Metro 0 -4.448 0.000117 -0.812
HMC_vs_Metro 1 -4.035 0.000364 -0.737
HMC_vs_Metro 2 -0.413 0.683 -0.075
HMC_vs_Metro 3 -4.239 0.000208 -0.774
HMC_vs_Metro 4 0.140 0.89 0.026
HMC_vs_SMC 0 -11.210 4.65e-12 -2.047
HMC_vs_SMC 1 -58.075 1.46e-31 -10.603
HMC_vs_SMC 2 -128.213 1.7e-41 -23.408
HMC_vs_SMC 3 -151.190 1.44e-43 -27.603
HMC_vs_SMC 4 -30.815 1.03e-23 -5.626
Metro_vs_SMC 0 -9.129 5e-10 -1.667
Metro_vs_SMC 1 -58.011 1.51e-31 -10.591
Metro_vs_SMC 2 -133.374 5.43e-42 -24.351
Metro_vs_SMC 3 -142.973 7.26e-43 -26.103
Metro_vs_SMC 4 -132.688 6.3e-42 -24.225
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.141 0.124 0.035 0.504
HMC 5 0.166 0.122 0.023 1.918
HMC 10 0.281 0.117 0.017 9.677
HMC 15 0.286 0.131 0.052 3.006
HMC 30 2.108 0.117 0.018 111.810
SMC 2 0.777 0.124 0.035 18.687
SMC 5 18.377 0.122 0.023 797.447
SMC 10 33.031 0.117 0.017 1946.292
SMC 15 38.058 0.131 0.052 735.400
SMC 30 42.165 0.117 0.018 2362.188
Metro 2 0.223 0.124 0.035 2.831
Metro 5 0.246 0.122 0.023 5.386
Metro 10 0.313 0.117 0.017 11.596
Metro 15 0.726 0.131 0.052 11.545
Metro 30 1.919 0.117 0.018 101.214
DEMetro_Z 2 0.271 0.124 0.035 4.196
DEMetro_Z 5 8.067 0.122 0.023 347.088
DEMetro_Z 10 12.568 0.117 0.017 736.254
DEMetro_Z 15 14.895 0.131 0.052 286.270
DEMetro_Z 30 20.752 0.117 0.018 1159.241
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 2.577 0.0126 0.622
HMC 5 2.833 0.00811 3.416
HMC 10 3.410 0.00192 11.982
HMC 15 4.879 3.52e-05 19.460
HMC 30 5.326 1.02e-05 31.396
SMC 2 15.858 5.19e-16 28.421
SMC 5 135.948 9.59e-44 169.340
SMC 10 112.025 1.51e-40 190.649
SMC 15 157.935 1.23e-45 201.511
SMC 30 195.178 7.43e-50 182.632
Metro 2 8.438 2.83e-10 4.082
Metro 5 12.179 8.38e-14 8.494
Metro 10 9.311 2.83e-10 20.141
Metro 15 7.836 1.2e-08 45.706
Metro 30 11.869 1.17e-12 92.345
DEMetro_Z 2 9.159 1.18e-10 6.149
DEMetro_Z 5 19.172 4.97e-18 131.204
DEMetro_Z 10 74.572 6.43e-35 210.492
DEMetro_Z 15 70.838 3.26e-34 230.853
DEMetro_Z 30 82.076 3.77e-36 222.806
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 -11.162 5.15e-12 -2.038
DEMetro_Z_vs_SMC 1 -5.515 6.07e-06 -1.007
DEMetro_Z_vs_SMC 2 6.305 6.93e-07 1.151
DEMetro_Z_vs_SMC 3 8.871 9.28e-10 1.620
DEMetro_Z_vs_SMC 4 14.048 1.8e-14 2.565
HMC_vs_Metro 0 -7.200 6.31e-08 -1.315
HMC_vs_Metro 1 -4.040 0.000358 -0.738
HMC_vs_Metro 2 -1.902 0.0672 -0.347
HMC_vs_Metro 3 -4.430 0.000123 -0.809
HMC_vs_Metro 4 -5.908 2.05e-06 -1.079
Metro_vs_DEMetro_Z 0 -2.476 0.0194 -0.452
Metro_vs_DEMetro_Z 1 -18.286 1.83e-17 -3.339
Metro_vs_DEMetro_Z 2 -54.215 1.05e-30 -9.898
Metro_vs_DEMetro_Z 3 -31.872 3.99e-24 -5.819
Metro_vs_DEMetro_Z 4 -14.926 3.81e-15 -2.725
HMC_vs_SMC 0 -15.617 1.18e-15 -2.851
HMC_vs_SMC 1 -98.216 3.8e-38 -17.932
HMC_vs_SMC 2 -46.081 1.11e-28 -8.413
HMC_vs_SMC 3 -43.979 4.23e-28 -8.030
HMC_vs_SMC 4 -25.132 3.1e-21 -4.588
Metro_vs_SMC 0 -12.998 1.27e-13 -2.373
Metro_vs_SMC 1 -114.396 4.62e-40 -20.886
Metro_vs_SMC 2 -61.304 3.07e-32 -11.193
Metro_vs_SMC 3 -27.216 3.37e-22 -4.969
Metro_vs_SMC 4 -11.663 1.8e-12 -2.129
HMC_vs_DEMetro_Z 0 -8.238 4.4e-09 -1.504
HMC_vs_DEMetro_Z 1 -18.826 8.41e-18 -3.437
HMC_vs_DEMetro_Z 2 -46.488 8.66e-29 -8.488
HMC_vs_DEMetro_Z 3 -40.121 5.82e-27 -7.325
HMC_vs_DEMetro_Z 4 -29.982 2.24e-23 -5.474
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.018 0.015 0.005 0.622
HMC 5 0.024 0.015 0.003 3.416
HMC 10 0.043 0.015 0.002 11.982
HMC 15 0.056 0.015 0.002 19.460
HMC 30 0.083 0.016 0.002 31.396
SMC 2 0.144 0.015 0.005 28.421
SMC 5 0.501 0.015 0.003 169.340
SMC 10 0.455 0.015 0.002 190.649
SMC 15 0.432 0.015 0.002 201.511
SMC 30 0.409 0.016 0.002 182.632
Metro 2 0.033 0.015 0.005 4.082
Metro 5 0.039 0.015 0.003 8.494
Metro 10 0.062 0.015 0.002 20.141
Metro 15 0.110 0.015 0.002 45.706
Metro 30 0.214 0.016 0.002 92.345
DEMetro_Z 2 0.043 0.015 0.005 6.149
DEMetro_Z 5 0.391 0.015 0.003 131.204
DEMetro_Z 10 0.500 0.015 0.002 210.492
DEMetro_Z 15 0.492 0.015 0.002 230.853
DEMetro_Z 30 0.495 0.016 0.002 222.806
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 0.306 0.76 0.085
HMC 5 0.511 0.612 0.294
HMC 10 1.242 0.224 2.880
HMC 15 1.151 0.259 5.500
HMC 30 2.090 0.0452 2.994
SMC 2 1.229 0.225 0.444
SMC 5 7.433 3.4e-08 55.326
SMC 10 6.763 2.01e-07 76.018
SMC 15 12.982 9.16e-14 22.368
SMC 30 33.659 6.52e-25 105.705
Metro 2 1.905 0.0631 0.725
Metro 5 2.961 0.00575 2.474
Metro 10 5.879 1.63e-06 5.248
Metro 15 2.299 0.0286 2.829
Metro 30 6.695 2.22e-07 13.216
DEMetro_Z 2 3.653 0.000765 1.736
DEMetro_Z 5 2.941 0.00636 59.803
DEMetro_Z 10 9.153 4.72e-10 187.133
DEMetro_Z 15 13.969 1.99e-14 72.707
DEMetro_Z 30 21.464 2.39e-19 495.568
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -3.590 0.0012 -0.656
HMC_vs_DEMetro_Z 1 -2.916 0.00678 -0.532
HMC_vs_DEMetro_Z 2 -8.956 7.57e-10 -1.635
HMC_vs_DEMetro_Z 3 -10.261 3.67e-11 -1.873
HMC_vs_DEMetro_Z 4 -20.791 5.73e-19 -3.796
Metro_vs_SMC 0 0.648 0.522 0.118
Metro_vs_SMC 1 -7.120 7.79e-08 -1.300
Metro_vs_SMC 2 -6.258 7.87e-07 -1.143
Metro_vs_SMC 3 -8.588 1.85e-09 -1.568
Metro_vs_SMC 4 -26.866 4.84e-22 -4.905
Metro_vs_DEMetro_Z 0 -1.675 0.105 -0.306
Metro_vs_DEMetro_Z 1 -2.821 0.00855 -0.515
Metro_vs_DEMetro_Z 2 -8.803 1.1e-09 -1.607
Metro_vs_DEMetro_Z 3 -12.837 1.73e-13 -2.344
Metro_vs_DEMetro_Z 4 -21.324 2.87e-19 -3.893
HMC_vs_Metro 0 -1.564 0.129 -0.286
HMC_vs_Metro 1 -2.295 0.0292 -0.419
HMC_vs_Metro 2 -0.923 0.364 -0.169
HMC_vs_Metro 3 0.531 0.599 0.097
HMC_vs_Metro 4 -3.911 0.000509 -0.714
HMC_vs_SMC 0 -0.997 0.327 -0.182
HMC_vs_SMC 1 -7.372 4.03e-08 -1.346
HMC_vs_SMC 2 -6.328 6.51e-07 -1.155
HMC_vs_SMC 3 -3.281 0.0027 -0.599
HMC_vs_SMC 4 -27.450 2.65e-22 -5.012
DEMetro_Z_vs_SMC 0 2.472 0.0196 0.451
DEMetro_Z_vs_SMC 1 0.208 0.837 0.038
DEMetro_Z_vs_SMC 2 5.758 3.1e-06 1.051
DEMetro_Z_vs_SMC 3 9.982 6.88e-11 1.822
DEMetro_Z_vs_SMC 4 16.840 1.64e-16 3.075
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.068 0.065 0.042 0.085
HMC 5 0.069 0.064 0.020 0.294
HMC 10 0.104 0.061 0.015 2.880
HMC 15 0.370 0.073 0.054 5.500
HMC 30 0.111 0.064 0.016 2.994
SMC 2 0.083 0.065 0.042 0.444
SMC 5 1.181 0.064 0.020 55.326
SMC 10 1.188 0.061 0.015 76.018
SMC 15 1.279 0.073 0.054 22.368
SMC 30 1.734 0.064 0.016 105.705
Metro 2 0.095 0.065 0.042 0.725
Metro 5 0.113 0.064 0.020 2.474
Metro 10 0.139 0.061 0.015 5.248
Metro 15 0.226 0.073 0.054 2.829
Metro 30 0.273 0.064 0.016 13.216
DEMetro_Z 2 0.138 0.065 0.042 1.736
DEMetro_Z 5 1.271 0.064 0.020 59.803
DEMetro_Z 10 2.836 0.061 0.015 187.133
DEMetro_Z 15 3.993 0.073 0.054 72.707
DEMetro_Z 30 7.895 0.064 0.016 495.568
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 -1.831 0.0757 -0.351
HMC 5 -2.040 0.0473 -0.424
HMC 10 -0.078 0.938 -0.019
HMC 15 -0.635 0.53 -0.123
HMC 30 2.227 0.0328 1.499
SMC 2 -0.422 0.676 -0.081
SMC 5 13.844 2.47e-14 63.119
SMC 10 27.610 2.2e-22 265.437
SMC 15 55.738 1.28e-51 15.254
SMC 30 88.508 7.17e-37 696.555
Metro 2 -1.738 0.0913 -0.330
Metro 5 -0.967 0.338 -0.217
Metro 10 1.017 0.313 0.241
Metro 15 -0.574 0.569 -0.114
Metro 30 3.238 0.00287 3.274
DEMetro_Z 2 -1.592 0.121 -0.304
DEMetro_Z 5 1.352 0.187 29.668
DEMetro_Z 10 4.109 0.000297 45.320
DEMetro_Z 15 4.760 2.14e-05 1.877
DEMetro_Z 30 9.055 5.95e-10 104.150
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -3.475 0.00163 -0.635
HMC_vs_SMC 1 -13.994 1.98e-14 -2.555
HMC_vs_SMC 2 -27.587 2.31e-22 -5.037
HMC_vs_SMC 3 -71.631 3.46e-34 -13.078
HMC_vs_SMC 4 -87.946 9.26e-37 -16.057
Metro_vs_DEMetro_Z 0 -1.384 0.177 -0.253
Metro_vs_DEMetro_Z 1 -1.362 0.184 -0.249
Metro_vs_DEMetro_Z 2 -4.118 0.00029 -0.752
Metro_vs_DEMetro_Z 3 -5.597 4.84e-06 -1.022
Metro_vs_DEMetro_Z 4 -8.865 9.42e-10 -1.619
HMC_vs_Metro 0 -0.663 0.512 -0.121
HMC_vs_Metro 1 -2.098 0.0447 -0.383
HMC_vs_Metro 2 -1.621 0.116 -0.296
HMC_vs_Metro 3 -0.090 0.929 -0.017
HMC_vs_Metro 4 -1.434 0.162 -0.262
HMC_vs_DEMetro_Z 0 -1.644 0.111 -0.300
HMC_vs_DEMetro_Z 1 -1.372 0.181 -0.250
HMC_vs_DEMetro_Z 2 -4.115 0.000292 -0.751
HMC_vs_DEMetro_Z 3 -5.494 6.44e-06 -1.003
HMC_vs_DEMetro_Z 4 -8.824 1.04e-09 -1.611
Metro_vs_SMC 0 -3.238 0.00301 -0.591
Metro_vs_SMC 1 -14.071 1.73e-14 -2.569
Metro_vs_SMC 2 -27.582 2.32e-22 -5.036
Metro_vs_SMC 3 -67.788 1.7e-33 -12.376
Metro_vs_SMC 4 -89.288 5.98e-37 -16.302
DEMetro_Z_vs_SMC 0 -2.951 0.00621 -0.539
DEMetro_Z_vs_SMC 1 -1.481 0.149 -0.270
DEMetro_Z_vs_SMC 2 -14.867 4.22e-15 -2.714
DEMetro_Z_vs_SMC 3 -32.142 3.15e-24 -5.868
DEMetro_Z_vs_SMC 4 -41.667 1.98e-27 -7.607
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 4.113 9.112 14.240 -0.351
HMC 5 4.972 8.258 7.752 -0.424
HMC 10 5.776 5.887 5.869 -0.019
HMC 15 15.662 33.673 146.019 -0.123
HMC 30 11.456 5.303 4.104 1.499
SMC 2 7.953 9.112 14.240 -0.081
SMC 5 497.557 8.258 7.752 63.119
SMC 10 1563.684 5.887 5.869 265.437
SMC 15 2260.978 33.673 146.019 15.254
SMC 30 2864.137 5.303 4.104 696.555
Metro 2 4.407 9.112 14.240 -0.330
Metro 5 6.573 8.258 7.752 -0.217
Metro 10 7.302 5.887 5.869 0.241
Metro 15 17.043 33.673 146.019 -0.114
Metro 30 18.741 5.303 4.104 3.274
DEMetro_Z 2 4.787 9.112 14.240 -0.304
DEMetro_Z 5 238.239 8.258 7.752 29.668
DEMetro_Z 10 271.860 5.887 5.869 45.320
DEMetro_Z 15 307.782 33.673 146.019 1.877
DEMetro_Z 30 432.759 5.303 4.104 104.150
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 1.885 0.067 0.889
HMC 5 2.387 0.0227 1.531
HMC 10 2.188 0.0368 6.846
HMC 15 1.638 0.112 9.730
HMC 30 2.887 0.00726 22.632
SMC 2 8.326 2.73e-09 11.831
SMC 5 23.847 1.32e-20 604.960
SMC 10 45.857 1.28e-28 1707.268
SMC 15 139.774 1.12e-42 695.164
SMC 30 168.272 6.28e-45 2302.342
Metro 2 6.480 4.11e-08 2.194
Metro 5 7.318 2.13e-08 5.267
Metro 10 5.212 1.37e-05 14.245
Metro 15 3.331 0.00235 8.222
Metro 30 4.235 0.00021 53.019
DEMetro_Z 2 8.369 2.04e-10 3.610
DEMetro_Z 5 3.393 0.00201 117.458
DEMetro_Z 10 7.216 6.05e-08 478.186
DEMetro_Z 15 11.598 2.06e-12 206.654
DEMetro_Z 30 17.336 7.6e-17 817.201
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -3.057 0.00477 -0.558
Metro_vs_DEMetro_Z 1 -3.237 0.00302 -0.591
Metro_vs_DEMetro_Z 2 -7.083 8.6e-08 -1.293
Metro_vs_DEMetro_Z 3 -10.971 7.74e-12 -2.003
Metro_vs_DEMetro_Z 4 -16.575 2.49e-16 -3.026
DEMetro_Z_vs_SMC 0 -5.854 2.38e-06 -1.069
DEMetro_Z_vs_SMC 1 -11.489 2.59e-12 -2.098
DEMetro_Z_vs_SMC 2 -15.623 1.17e-15 -2.852
DEMetro_Z_vs_SMC 3 -25.565 1.93e-21 -4.667
DEMetro_Z_vs_SMC 4 -30.003 2.19e-23 -5.478
HMC_vs_DEMetro_Z 0 -5.513 6.1e-06 -1.007
HMC_vs_DEMetro_Z 1 -3.342 0.0023 -0.610
HMC_vs_DEMetro_Z 2 -7.119 7.81e-08 -1.300
HMC_vs_DEMetro_Z 3 -10.527 2.03e-11 -1.922
HMC_vs_DEMetro_Z 4 -15.700 1.03e-15 -2.866
HMC_vs_Metro 0 -2.499 0.0184 -0.456
HMC_vs_Metro 1 -3.749 0.000787 -0.684
HMC_vs_Metro 2 -1.653 0.109 -0.302
HMC_vs_Metro 3 0.226 0.823 0.041
HMC_vs_Metro 4 -1.925 0.0641 -0.351
HMC_vs_SMC 0 -7.978 8.47e-09 -1.457
HMC_vs_SMC 1 -23.701 1.57e-20 -4.327
HMC_vs_SMC 2 -45.538 1.56e-28 -8.314
HMC_vs_SMC 3 -85.711 1.95e-36 -15.649
HMC_vs_SMC 4 -148.053 2.64e-43 -27.031
Metro_vs_SMC 0 -6.659 2.66e-07 -1.216
Metro_vs_SMC 1 -23.907 1.24e-20 -4.365
Metro_vs_SMC 2 -45.436 1.67e-28 -8.295
Metro_vs_SMC 3 -119.356 1.35e-40 -21.791
Metro_vs_SMC 4 -131.482 8.21e-42 -24.005
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.155 0.124 0.035 0.889
HMC 5 0.157 0.122 0.023 1.531
HMC 10 0.233 0.117 0.017 6.846
HMC 15 0.633 0.131 0.052 9.730
HMC 30 0.520 0.117 0.018 22.632
SMC 2 0.537 0.124 0.035 11.831
SMC 5 13.970 0.122 0.023 604.960
SMC 10 28.989 0.117 0.017 1707.268
SMC 15 35.983 0.131 0.052 695.164
SMC 30 41.099 0.117 0.018 2302.342
Metro 2 0.201 0.124 0.035 2.194
Metro 5 0.243 0.122 0.023 5.267
Metro 10 0.358 0.117 0.017 14.245
Metro 15 0.555 0.131 0.052 8.222
Metro 30 1.061 0.117 0.018 53.019
DEMetro_Z 2 0.250 0.124 0.035 3.610
DEMetro_Z 5 2.811 0.122 0.023 117.458
DEMetro_Z 10 8.204 0.117 0.017 478.186
DEMetro_Z 15 10.789 0.131 0.052 206.654
DEMetro_Z 30 14.664 0.117 0.018 817.201
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 2.744 0.00835 0.891
HMC 5 1.782 0.0851 3.294
HMC 10 1.640 0.112 15.634
HMC 15 2.359 0.0253 32.959
HMC 30 3.191 0.0034 33.083
SMC 2 10.338 2.55e-11 20.641
SMC 5 90.327 1.21e-37 171.338
SMC 10 120.876 1.33e-41 196.155
SMC 15 166.860 1.88e-46 206.681
SMC 30 202.869 1.42e-50 184.386
Metro 2 8.019 7.36e-10 3.600
Metro 5 8.100 4.01e-09 8.572
Metro 10 5.926 1.91e-06 21.169
Metro 15 7.140 7.29e-08 38.412
Metro 30 6.659 2.64e-07 57.060
DEMetro_Z 2 9.289 2.65e-11 4.615
DEMetro_Z 5 7.949 9.06e-09 77.180
DEMetro_Z 10 20.890 4.94e-19 207.076
DEMetro_Z 15 34.008 6.07e-25 247.217
DEMetro_Z 30 51.895 3.18e-30 247.955
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 -8.018 7.66e-09 -1.464
DEMetro_Z_vs_SMC 1 -9.513 2.02e-10 -1.737
DEMetro_Z_vs_SMC 2 1.162 0.255 0.212
DEMetro_Z_vs_SMC 3 5.594 4.87e-06 1.021
DEMetro_Z_vs_SMC 4 13.677 3.54e-14 2.497
HMC_vs_Metro 0 -5.333 1.01e-05 -0.974
HMC_vs_Metro 1 -2.265 0.0312 -0.414
HMC_vs_Metro 2 -0.523 0.605 -0.095
HMC_vs_Metro 3 -0.339 0.737 -0.062
HMC_vs_Metro 4 -1.619 0.116 -0.296
Metro_vs_DEMetro_Z 0 -1.743 0.0919 -0.318
Metro_vs_DEMetro_Z 1 -7.062 9.08e-08 -1.289
Metro_vs_DEMetro_Z 2 -16.701 2.04e-16 -3.049
Metro_vs_DEMetro_Z 3 -25.465 2.15e-21 -4.649
Metro_vs_DEMetro_Z 4 -19.413 3.68e-18 -3.544
HMC_vs_SMC 0 -9.970 7.06e-11 -1.820
HMC_vs_SMC 1 -56.504 3.21e-31 -10.316
HMC_vs_SMC 2 -18.502 1.34e-17 -3.378
HMC_vs_SMC 3 -12.640 2.54e-13 -2.308
HMC_vs_SMC 4 -14.916 3.88e-15 -2.723
Metro_vs_SMC 0 -8.188 4.99e-09 -1.495
Metro_vs_SMC 1 -76.431 5.33e-35 -13.954
Metro_vs_SMC 2 -45.162 1.98e-28 -8.245
Metro_vs_SMC 3 -31.369 6.26e-24 -5.727
Metro_vs_SMC 4 -14.725 5.41e-15 -2.688
HMC_vs_DEMetro_Z 0 -6.969 1.16e-07 -1.272
HMC_vs_DEMetro_Z 1 -7.144 7.31e-08 -1.304
HMC_vs_DEMetro_Z 2 -13.865 2.51e-14 -2.531
HMC_vs_DEMetro_Z 3 -14.830 4.51e-15 -2.708
HMC_vs_DEMetro_Z 4 -22.448 7.03e-20 -4.098
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.019 0.015 0.005 0.891
HMC 5 0.024 0.015 0.003 3.294
HMC 10 0.051 0.015 0.002 15.634
HMC 15 0.083 0.015 0.002 32.959
HMC 30 0.087 0.016 0.002 33.083
SMC 2 0.108 0.015 0.005 20.641
SMC 5 0.507 0.015 0.003 171.338
SMC 10 0.467 0.015 0.002 196.155
SMC 15 0.443 0.015 0.002 206.681
SMC 30 0.413 0.016 0.002 184.386
Metro 2 0.031 0.015 0.005 3.600
Metro 5 0.039 0.015 0.003 8.572
Metro 10 0.064 0.015 0.002 21.169
Metro 15 0.095 0.015 0.002 38.412
Metro 30 0.138 0.016 0.002 57.060
DEMetro_Z 2 0.036 0.015 0.005 4.615
DEMetro_Z 5 0.236 0.015 0.003 77.180
DEMetro_Z 10 0.493 0.015 0.002 207.076
DEMetro_Z 15 0.526 0.015 0.002 247.217
DEMetro_Z 30 0.550 0.016 0.002 247.955
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
Trace Plots
Pooled
2 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
30 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
30 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2
5
10
15
30
Chain
2
5
10
15
30

Vary_Dimension_with_high_Multimodality (Mixture, dimension, 30 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 5.873 2.23e-06 23.747
HMC 5 7.342 4.21e-08 26.116
HMC 10 5.451 7.2e-06 28.380
HMC 15 5.482 6.58e-06 25.682
HMC 30 5.050 2.21e-05 50.088
SMC 2 0.595 0.554 0.163
SMC 5 -1.084 0.283 -0.255
SMC 10 -0.011 0.991 -0.003
SMC 15 0.349 0.728 0.086
SMC 30 1.080 0.286 0.396
Metro 2 6.913 1.32e-07 26.937
Metro 5 6.172 9.79e-07 26.555
Metro 10 6.337 6.26e-07 29.903
Metro 15 6.462 4.46e-07 31.635
Metro 30 5.321 1.04e-05 53.862
DEMetro_Z 2 5.997 1.56e-06 19.081
DEMetro_Z 5 11.694 1.64e-12 64.051
DEMetro_Z 10 22.919 3.91e-20 257.289
DEMetro_Z 15 22.361 7.74e-20 324.790
DEMetro_Z 30 33.417 1.04e-24 959.339
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 0.984 0.333 0.180
HMC_vs_DEMetro_Z 1 -5.545 5.59e-06 -1.012
HMC_vs_DEMetro_Z 2 -19.389 3.8e-18 -3.540
HMC_vs_DEMetro_Z 3 -19.954 1.75e-18 -3.643
HMC_vs_DEMetro_Z 4 -34.022 6.31e-25 -6.211
Metro_vs_SMC 0 6.832 1.67e-07 1.247
Metro_vs_SMC 1 6.255 7.93e-07 1.142
Metro_vs_SMC 2 6.299 7.03e-07 1.150
Metro_vs_SMC 3 6.465 4.49e-07 1.180
Metro_vs_SMC 4 5.296 1.11e-05 0.967
Metro_vs_DEMetro_Z 0 1.685 0.103 0.308
Metro_vs_DEMetro_Z 1 -5.346 9.7e-06 -0.976
Metro_vs_DEMetro_Z 2 -18.887 7.7e-18 -3.448
Metro_vs_DEMetro_Z 3 -19.721 2.4e-18 -3.600
Metro_vs_DEMetro_Z 4 -33.261 1.2e-24 -6.073
HMC_vs_Metro 0 -1.004 0.324 -0.183
HMC_vs_Metro 1 -0.136 0.893 -0.025
HMC_vs_Metro 2 -0.243 0.81 -0.044
HMC_vs_Metro 3 -0.890 0.381 -0.163
HMC_vs_Metro 4 -0.700 0.489 -0.128
HMC_vs_SMC 0 5.782 2.9e-06 1.056
HMC_vs_SMC 1 7.517 2.76e-08 1.372
HMC_vs_SMC 2 5.520 5.99e-06 1.008
HMC_vs_SMC 3 5.440 7.47e-06 0.993
HMC_vs_SMC 4 5.011 2.46e-05 0.915
DEMetro_Z_vs_SMC 0 5.932 1.92e-06 1.083
DEMetro_Z_vs_SMC 1 11.763 1.47e-12 2.148
DEMetro_Z_vs_SMC 2 23.004 3.58e-20 4.200
DEMetro_Z_vs_SMC 3 22.331 8.1e-20 4.077
DEMetro_Z_vs_SMC 4 33.376 1.09e-24 6.094
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 1.426 0.081 0.057 23.747
HMC 5 1.174 0.062 0.043 26.116
HMC 10 0.606 0.045 0.020 28.380
HMC 15 0.511 0.040 0.018 25.682
HMC 30 0.376 0.029 0.007 50.088
SMC 2 0.090 0.081 0.057 0.163
SMC 5 0.051 0.062 0.043 -0.255
SMC 10 0.045 0.045 0.020 -0.003
SMC 15 0.042 0.040 0.018 0.086
SMC 30 0.032 0.029 0.007 0.396
Metro 2 1.607 0.081 0.057 26.937
Metro 5 1.193 0.062 0.043 26.555
Metro 10 0.637 0.045 0.020 29.903
Metro 15 0.621 0.040 0.018 31.635
Metro 30 0.403 0.029 0.007 53.862
DEMetro_Z 2 1.162 0.081 0.057 19.081
DEMetro_Z 5 2.789 0.062 0.043 64.051
DEMetro_Z 10 5.137 0.045 0.020 257.289
DEMetro_Z 15 6.000 0.040 0.018 324.790
DEMetro_Z 30 6.683 0.029 0.007 959.339
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 4.375 0.000143 45.694
HMC 5 5.022 2.38e-05 61.701
HMC 10 4.160 0.000258 48.951
HMC 15 4.117 0.000291 51.350
HMC 30 3.903 0.00052 67.473
SMC 2 0.976 0.333 0.270
SMC 5 -0.635 0.528 -0.174
SMC 10 0.734 0.466 0.193
SMC 15 0.345 0.731 0.110
SMC 30 2.208 0.0321 0.784
Metro 2 4.837 3.98e-05 51.229
Metro 5 4.747 5.11e-05 72.973
Metro 10 4.764 4.88e-05 46.801
Metro 15 4.582 8.08e-05 68.283
Metro 30 4.002 0.000398 73.572
DEMetro_Z 2 3.439 0.00179 28.988
DEMetro_Z 5 6.972 1.15e-07 528.854
DEMetro_Z 10 19.614 2.78e-18 2637.129
DEMetro_Z 15 25.150 3.04e-21 4219.731
DEMetro_Z 30 33.455 1.01e-24 7619.194
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 4.372 0.000144 0.798
HMC_vs_SMC 1 5.021 2.39e-05 0.917
HMC_vs_SMC 2 4.159 0.000259 0.759
HMC_vs_SMC 3 4.109 0.000297 0.750
HMC_vs_SMC 4 3.852 0.000597 0.703
Metro_vs_DEMetro_Z 0 1.707 0.0985 0.312
Metro_vs_DEMetro_Z 1 -5.743 3.23e-06 -1.048
Metro_vs_DEMetro_Z 2 -18.925 7.3e-18 -3.455
Metro_vs_DEMetro_Z 3 -24.640 5.37e-21 -4.499
Metro_vs_DEMetro_Z 4 -32.369 2.58e-24 -5.910
HMC_vs_Metro 0 -0.992 0.329 -0.181
HMC_vs_Metro 1 -0.776 0.444 -0.142
HMC_vs_Metro 2 0.146 0.885 0.027
HMC_vs_Metro 3 -0.847 0.404 -0.155
HMC_vs_Metro 4 -0.644 0.524 -0.118
HMC_vs_DEMetro_Z 0 1.311 0.2 0.239
HMC_vs_DEMetro_Z 1 -5.970 1.73e-06 -1.090
HMC_vs_DEMetro_Z 2 -19.091 5.77e-18 -3.486
HMC_vs_DEMetro_Z 3 -24.631 5.42e-21 -4.497
HMC_vs_DEMetro_Z 4 -32.986 1.51e-24 -6.022
Metro_vs_SMC 0 4.845 3.91e-05 0.885
Metro_vs_SMC 1 4.767 4.85e-05 0.870
Metro_vs_SMC 2 4.719 5.53e-05 0.862
Metro_vs_SMC 3 4.578 8.18e-05 0.836
Metro_vs_SMC 4 3.964 0.000441 0.724
DEMetro_Z_vs_SMC 0 3.415 0.0019 0.624
DEMetro_Z_vs_SMC 1 6.972 1.15e-07 1.273
DEMetro_Z_vs_SMC 2 19.620 2.76e-18 3.582
DEMetro_Z_vs_SMC 3 25.159 3.01e-21 4.593
DEMetro_Z_vs_SMC 4 33.457 1.01e-24 6.108
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 5.137 0.141 0.109 45.694
HMC 5 4.613 0.114 0.073 61.701
HMC 10 2.218 0.076 0.044 48.951
HMC 15 1.811 0.071 0.034 51.350
HMC 30 1.571 0.052 0.023 67.473
SMC 2 0.170 0.141 0.109 0.270
SMC 5 0.101 0.114 0.073 -0.174
SMC 10 0.085 0.076 0.044 0.193
SMC 15 0.075 0.071 0.034 0.110
SMC 30 0.069 0.052 0.023 0.784
Metro 2 5.742 0.141 0.109 51.229
Metro 5 5.435 0.114 0.073 72.973
Metro 10 2.124 0.076 0.044 46.801
Metro 15 2.384 0.071 0.034 68.283
Metro 30 1.709 0.052 0.023 73.572
DEMetro_Z 2 3.310 0.141 0.109 28.988
DEMetro_Z 5 38.676 0.114 0.073 528.854
DEMetro_Z 10 115.465 0.076 0.044 2637.129
DEMetro_Z 15 142.987 0.071 0.034 4219.731
DEMetro_Z 30 171.651 0.052 0.023 7619.194
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 5.895 2.1e-06 27.181
HMC 5 7.056 9.05e-08 31.139
HMC 10 5.468 6.88e-06 33.848
HMC 15 5.441 7.39e-06 29.205
HMC 30 5.057 2.16e-05 61.765
SMC 2 0.549 0.585 0.152
SMC 5 -0.777 0.441 -0.183
SMC 10 0.587 0.559 0.169
SMC 15 0.080 0.937 0.019
SMC 30 1.694 0.0971 0.650
Metro 2 6.741 2.1e-07 29.851
Metro 5 6.135 1.09e-06 30.330
Metro 10 6.356 5.97e-07 36.174
Metro 15 6.377 5.64e-07 35.574
Metro 30 5.282 1.16e-05 67.357
DEMetro_Z 2 5.776 2.9e-06 21.376
DEMetro_Z 5 12.230 5.64e-13 112.530
DEMetro_Z 10 36.216 1.06e-25 593.375
DEMetro_Z 15 37.248 4.79e-26 690.302
DEMetro_Z 30 58.097 1.44e-31 2292.236
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 1.628 0.114 0.297
Metro_vs_DEMetro_Z 1 -7.675 1.84e-08 -1.401
Metro_vs_DEMetro_Z 2 -30.637 1.22e-23 -5.593
Metro_vs_DEMetro_Z 3 -34.058 6.12e-25 -6.218
Metro_vs_DEMetro_Z 4 -53.092 1.92e-30 -9.693
DEMetro_Z_vs_SMC 0 5.718 3.46e-06 1.044
DEMetro_Z_vs_SMC 1 12.249 5.49e-13 2.236
DEMetro_Z_vs_SMC 2 36.383 9.41e-26 6.643
DEMetro_Z_vs_SMC 3 37.191 5.04e-26 6.790
DEMetro_Z_vs_SMC 4 58.160 1.4e-31 10.619
HMC_vs_DEMetro_Z 0 1.070 0.293 0.195
HMC_vs_DEMetro_Z 1 -7.555 2.5e-08 -1.379
HMC_vs_DEMetro_Z 2 -32.684 1.96e-24 -5.967
HMC_vs_DEMetro_Z 3 -34.780 3.38e-25 -6.350
HMC_vs_DEMetro_Z 4 -56.929 2.59e-31 -10.394
HMC_vs_Metro 0 -0.739 0.466 -0.135
HMC_vs_Metro 1 0.197 0.845 0.036
HMC_vs_Metro 2 -0.311 0.758 -0.057
HMC_vs_Metro 3 -0.841 0.407 -0.153
HMC_vs_Metro 4 -0.785 0.439 -0.143
HMC_vs_SMC 0 5.815 2.65e-06 1.062
HMC_vs_SMC 1 7.191 6.46e-08 1.313
HMC_vs_SMC 2 5.512 6.12e-06 1.006
HMC_vs_SMC 3 5.416 8e-06 0.989
HMC_vs_SMC 4 5.001 2.53e-05 0.913
Metro_vs_SMC 0 6.653 2.7e-07 1.215
Metro_vs_SMC 1 6.192 9.41e-07 1.131
Metro_vs_SMC 2 6.302 6.97e-07 1.151
Metro_vs_SMC 3 6.390 5.5e-07 1.167
Metro_vs_SMC 4 5.239 1.31e-05 0.956
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 1.320 0.090 0.045 27.181
HMC 5 1.030 0.066 0.031 31.139
HMC 10 0.490 0.050 0.013 33.848
HMC 15 0.422 0.047 0.013 29.205
HMC 30 0.308 0.037 0.004 61.765
SMC 2 0.097 0.090 0.045 0.152
SMC 5 0.061 0.066 0.031 -0.183
SMC 10 0.052 0.050 0.013 0.169
SMC 15 0.047 0.047 0.013 0.019
SMC 30 0.040 0.037 0.004 0.650
Metro 2 1.440 0.090 0.045 29.851
Metro 5 1.005 0.066 0.031 30.330
Metro 10 0.520 0.050 0.013 36.174
Metro 15 0.503 0.047 0.013 35.574
Metro 30 0.332 0.037 0.004 67.357
DEMetro_Z 2 1.057 0.090 0.045 21.376
DEMetro_Z 5 3.550 0.066 0.031 112.530
DEMetro_Z 10 7.760 0.050 0.013 593.375
DEMetro_Z 15 8.894 0.047 0.013 690.302
DEMetro_Z 30 10.087 0.037 0.004 2292.236
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 5.905 2.04e-06 28.145
HMC 5 7.498 2.82e-08 30.428
HMC 10 5.448 7.27e-06 33.214
HMC 15 5.517 6e-06 32.594
HMC 30 5.088 1.99e-05 62.016
SMC 2 1.103 0.275 0.304
SMC 5 -1.096 0.278 -0.255
SMC 10 0.294 0.77 0.080
SMC 15 0.300 0.765 0.076
SMC 30 1.787 0.081 0.712
Metro 2 7.194 6.29e-08 32.076
Metro 5 6.263 7.67e-07 30.938
Metro 10 6.385 5.51e-07 35.545
Metro 15 6.470 4.39e-07 40.020
Metro 30 5.267 1.21e-05 68.195
DEMetro_Z 2 6.181 9.51e-07 23.167
DEMetro_Z 5 22.203 6.3e-20 48.017
DEMetro_Z 10 61.524 8.48e-33 110.471
DEMetro_Z 15 72.073 5.34e-35 112.647
DEMetro_Z 30 80.723 6.89e-36 245.154
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 6.111 1.18e-06 1.116
DEMetro_Z_vs_SMC 1 22.546 6.23e-20 4.116
DEMetro_Z_vs_SMC 2 61.763 2.48e-32 11.276
DEMetro_Z_vs_SMC 3 72.060 2.92e-34 13.156
DEMetro_Z_vs_SMC 4 80.823 1.06e-35 14.756
HMC_vs_Metro 0 -1.018 0.317 -0.186
HMC_vs_Metro 1 -0.138 0.891 -0.025
HMC_vs_Metro 2 -0.318 0.753 -0.058
HMC_vs_Metro 3 -0.875 0.389 -0.160
HMC_vs_Metro 4 -0.878 0.387 -0.160
Metro_vs_DEMetro_Z 0 1.658 0.108 0.303
Metro_vs_DEMetro_Z 1 -3.230 0.00307 -0.590
Metro_vs_DEMetro_Z 2 -12.595 2.77e-13 -2.299
Metro_vs_DEMetro_Z 3 -11.285 3.97e-12 -2.060
Metro_vs_DEMetro_Z 4 -15.442 1.59e-15 -2.819
HMC_vs_SMC 0 5.801 2.75e-06 1.059
HMC_vs_SMC 1 7.647 1.97e-08 1.396
HMC_vs_SMC 2 5.490 6.51e-06 1.002
HMC_vs_SMC 3 5.483 6.63e-06 1.001
HMC_vs_SMC 4 5.025 2.36e-05 0.917
Metro_vs_SMC 0 7.104 8.14e-08 1.297
Metro_vs_SMC 1 6.339 6.31e-07 1.157
Metro_vs_SMC 2 6.328 6.5e-07 1.155
Metro_vs_SMC 3 6.478 4.33e-07 1.183
Metro_vs_SMC 4 5.218 1.38e-05 0.953
HMC_vs_DEMetro_Z 0 0.882 0.385 0.161
HMC_vs_DEMetro_Z 1 -3.777 0.00073 -0.690
HMC_vs_DEMetro_Z 2 -13.426 5.65e-14 -2.451
HMC_vs_DEMetro_Z 3 -13.070 1.11e-13 -2.386
HMC_vs_DEMetro_Z 4 -15.656 1.11e-15 -2.858
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.216 0.012 0.007 28.145
HMC 5 0.267 0.014 0.008 30.428
HMC 10 0.181 0.014 0.005 33.214
HMC 15 0.177 0.014 0.005 32.594
HMC 30 0.154 0.013 0.002 62.016
SMC 2 0.014 0.012 0.007 0.304
SMC 5 0.012 0.014 0.008 -0.255
SMC 10 0.014 0.014 0.005 0.080
SMC 15 0.015 0.014 0.005 0.076
SMC 30 0.015 0.013 0.002 0.712
Metro 2 0.245 0.012 0.007 32.076
Metro 5 0.271 0.014 0.008 30.938
Metro 10 0.193 0.014 0.005 35.545
Metro 15 0.214 0.014 0.005 40.020
Metro 30 0.168 0.013 0.002 68.195
DEMetro_Z 2 0.180 0.012 0.007 23.167
DEMetro_Z 5 0.413 0.014 0.008 48.017
DEMetro_Z 10 0.570 0.014 0.005 110.471
DEMetro_Z 15 0.575 0.014 0.005 112.647
DEMetro_Z 30 0.570 0.013 0.002 245.154
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 256.602 9.06e-88 73.419
HMC 5 237.665 2.19e-88 61.459
HMC 10 274.370 1.18e-79 93.868
HMC 15 230.589 6.71e-74 82.098
HMC 30 303.731 3.99e-65 154.016
SMC 2 0.383 0.703 0.103
SMC 5 -1.574 0.121 -0.374
SMC 10 -0.492 0.625 -0.139
SMC 15 -0.043 0.966 -0.011
SMC 30 0.204 0.839 0.059
Metro 2 37.272 2.14e-26 70.750
Metro 5 20.722 4.92e-19 56.376
Metro 10 21.708 1.56e-19 85.652
Metro 15 20.459 7.74e-19 73.883
Metro 30 24.601 5.27e-21 142.986
DEMetro_Z 2 17.177 8.78e-17 66.312
DEMetro_Z 5 24.001 8.57e-21 67.428
DEMetro_Z 10 15.321 1.94e-15 344.334
DEMetro_Z 15 16.626 2.29e-16 517.736
DEMetro_Z 30 22.885 4.13e-20 1580.627
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 1.867 0.072 0.341
HMC_vs_DEMetro_Z 1 -2.119 0.0428 -0.387
HMC_vs_DEMetro_Z 2 -11.149 5.3e-12 -2.035
HMC_vs_DEMetro_Z 3 -13.989 2e-14 -2.554
HMC_vs_DEMetro_Z 4 -20.678 6.64e-19 -3.775
Metro_vs_SMC 0 36.665 7.56e-26 6.694
Metro_vs_SMC 1 21.000 4.36e-19 3.834
Metro_vs_SMC 2 21.445 2.46e-19 3.915
Metro_vs_SMC 3 20.753 6.02e-19 3.789
Metro_vs_SMC 4 24.451 6.64e-21 4.464
Metro_vs_DEMetro_Z 0 1.006 0.323 0.184
Metro_vs_DEMetro_Z 1 -2.995 0.00557 -0.547
Metro_vs_DEMetro_Z 2 -11.555 2.25e-12 -2.110
Metro_vs_DEMetro_Z 3 -14.588 6.88e-15 -2.663
Metro_vs_DEMetro_Z 4 -20.882 5.08e-19 -3.813
HMC_vs_Metro 0 1.400 0.172 0.256
HMC_vs_Metro 1 1.865 0.0723 0.341
HMC_vs_Metro 2 2.108 0.0438 0.385
HMC_vs_Metro 3 2.254 0.0319 0.412
HMC_vs_Metro 4 1.924 0.0642 0.351
HMC_vs_SMC 0 293.488 6.45e-52 53.583
HMC_vs_SMC 1 251.236 5.84e-50 45.869
HMC_vs_SMC 2 292.154 7.36e-52 53.340
HMC_vs_SMC 3 233.975 4.6e-49 42.718
HMC_vs_SMC 4 308.528 1.51e-52 56.329
DEMetro_Z_vs_SMC 0 17.198 9.39e-17 3.140
DEMetro_Z_vs_SMC 1 24.054 1.05e-20 4.392
DEMetro_Z_vs_SMC 2 15.331 1.91e-15 2.799
DEMetro_Z_vs_SMC 3 16.619 2.32e-16 3.034
DEMetro_Z_vs_SMC 4 22.877 4.17e-20 4.177
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 4.241 0.081 0.057 73.419
HMC 5 2.679 0.062 0.043 61.459
HMC 10 1.903 0.045 0.020 93.868
HMC 15 1.547 0.040 0.018 82.098
HMC 30 1.097 0.029 0.007 154.016
SMC 2 0.087 0.081 0.057 0.103
SMC 5 0.046 0.062 0.043 -0.374
SMC 10 0.042 0.045 0.020 -0.139
SMC 15 0.040 0.040 0.018 -0.011
SMC 30 0.029 0.029 0.007 0.059
Metro 2 4.089 0.081 0.057 70.750
Metro 5 2.463 0.062 0.043 56.376
Metro 10 1.740 0.045 0.020 85.652
Metro 15 1.396 0.040 0.018 73.883
Metro 30 1.021 0.029 0.007 142.986
DEMetro_Z 2 3.838 0.081 0.057 66.312
DEMetro_Z 5 2.933 0.062 0.043 67.428
DEMetro_Z 10 6.860 0.045 0.020 344.334
DEMetro_Z 15 9.540 0.040 0.018 517.736
DEMetro_Z 30 10.992 0.029 0.007 1580.627
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 785.937 3.07e-113 231.262
HMC 5 766.048 2.24e-114 219.243
HMC 10 864.675 2.43e-114 258.731
HMC 15 882.601 1.8e-112 272.540
HMC 30 791.204 2.66e-97 289.649
SMC 2 0.883 0.381 0.233
SMC 5 -0.940 0.351 -0.219
SMC 10 0.579 0.565 0.145
SMC 15 -0.095 0.925 -0.024
SMC 30 0.912 0.366 0.316
Metro 2 28.631 7.83e-23 219.664
Metro 5 17.594 5.07e-17 195.339
Metro 10 16.431 3.11e-16 229.509
Metro 15 16.383 3.36e-16 236.741
Metro 30 18.172 2.15e-17 260.372
DEMetro_Z 2 16.320 3.71e-16 208.282
DEMetro_Z 5 14.678 5.85e-15 237.134
DEMetro_Z 10 10.720 1.33e-11 534.623
DEMetro_Z 15 10.969 7.77e-12 651.708
DEMetro_Z 30 14.187 1.4e-14 941.299
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 662.577 3.59e-62 120.969
HMC_vs_SMC 1 710.202 4.8e-63 129.665
HMC_vs_SMC 2 1056.297 4.81e-68 192.853
HMC_vs_SMC 3 949.916 1.04e-66 173.430
HMC_vs_SMC 4 882.731 8.76e-66 161.164
Metro_vs_DEMetro_Z 0 0.733 0.469 0.134
Metro_vs_DEMetro_Z 1 -1.976 0.0578 -0.361
Metro_vs_DEMetro_Z 2 -6.348 6.17e-07 -1.159
Metro_vs_DEMetro_Z 3 -6.403 5.31e-07 -1.169
Metro_vs_DEMetro_Z 4 -10.496 2.17e-11 -1.916
HMC_vs_Metro 0 1.519 0.14 0.277
HMC_vs_Metro 1 2.148 0.0402 0.392
HMC_vs_Metro 2 2.099 0.0446 0.383
HMC_vs_Metro 3 2.484 0.019 0.453
HMC_vs_Metro 4 2.038 0.0508 0.372
HMC_vs_DEMetro_Z 0 1.791 0.0837 0.327
HMC_vs_DEMetro_Z 1 -1.107 0.277 -0.202
HMC_vs_DEMetro_Z 2 -5.525 5.9e-06 -1.009
HMC_vs_DEMetro_Z 3 -6.381 5.63e-07 -1.165
HMC_vs_DEMetro_Z 4 -9.831 9.7e-11 -1.795
Metro_vs_SMC 0 28.412 1.01e-22 5.187
Metro_vs_SMC 1 17.688 4.45e-17 3.229
Metro_vs_SMC 2 16.442 3.08e-16 3.002
Metro_vs_SMC 3 16.382 3.39e-16 2.991
Metro_vs_SMC 4 18.083 2.47e-17 3.301
DEMetro_Z_vs_SMC 0 16.323 3.72e-16 2.980
DEMetro_Z_vs_SMC 1 14.669 5.96e-15 2.678
DEMetro_Z_vs_SMC 2 10.711 1.36e-11 1.956
DEMetro_Z_vs_SMC 3 10.972 7.73e-12 2.003
DEMetro_Z_vs_SMC 4 14.188 1.4e-14 2.590
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 25.429 0.141 0.109 231.262
HMC 5 16.100 0.114 0.073 219.243
HMC 10 11.397 0.076 0.044 258.731
HMC 15 9.302 0.071 0.034 272.540
HMC 30 6.575 0.052 0.023 289.649
SMC 2 0.166 0.141 0.109 0.233
SMC 5 0.098 0.114 0.073 -0.219
SMC 10 0.083 0.076 0.044 0.145
SMC 15 0.071 0.071 0.034 -0.024
SMC 30 0.059 0.052 0.023 0.316
Metro 2 24.161 0.141 0.109 219.664
Metro 5 14.357 0.114 0.073 195.339
Metro 10 10.119 0.076 0.044 229.509
Metro 15 8.089 0.071 0.034 236.741
Metro 30 5.916 0.052 0.023 260.372
DEMetro_Z 2 22.916 0.141 0.109 208.282
DEMetro_Z 5 17.405 0.114 0.073 237.134
DEMetro_Z 10 23.469 0.076 0.044 534.623
DEMetro_Z 15 22.144 0.071 0.034 651.708
DEMetro_Z 30 21.252 0.052 0.023 941.299
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 79.448 3.38e-37 83.686
HMC 5 59.043 5.86e-33 69.323
HMC 10 82.996 5.51e-37 117.814
HMC 15 81.829 2.65e-37 94.223
HMC 30 133.122 4.55e-43 193.248
SMC 2 0.676 0.502 0.183
SMC 5 -1.358 0.18 -0.315
SMC 10 -0.076 0.94 -0.022
SMC 15 -0.333 0.741 -0.086
SMC 30 0.456 0.65 0.132
Metro 2 33.627 5.45e-25 79.522
Metro 5 19.618 2.38e-18 65.918
Metro 10 20.415 8.81e-19 107.118
Metro 15 19.557 2.73e-18 82.015
Metro 30 24.596 5.43e-21 179.603
DEMetro_Z 2 17.178 8.95e-17 74.369
DEMetro_Z 5 20.905 4.36e-19 80.421
DEMetro_Z 10 16.148 4.93e-16 443.844
DEMetro_Z 15 16.470 2.94e-16 623.115
DEMetro_Z 30 22.834 4.39e-20 2082.460
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 1.015 0.319 0.185
Metro_vs_DEMetro_Z 1 -2.864 0.00769 -0.523
Metro_vs_DEMetro_Z 2 -12.264 5.33e-13 -2.239
Metro_vs_DEMetro_Z 3 -14.779 4.92e-15 -2.698
Metro_vs_DEMetro_Z 4 -20.967 4.55e-19 -3.828
DEMetro_Z_vs_SMC 0 17.197 9.4e-17 3.140
DEMetro_Z_vs_SMC 1 20.935 4.74e-19 3.822
DEMetro_Z_vs_SMC 2 16.154 4.89e-16 2.949
DEMetro_Z_vs_SMC 3 16.465 2.96e-16 3.006
DEMetro_Z_vs_SMC 4 22.823 4.46e-20 4.167
HMC_vs_DEMetro_Z 0 2.123 0.0424 0.388
HMC_vs_DEMetro_Z 1 -2.770 0.00969 -0.506
HMC_vs_DEMetro_Z 2 -11.788 1.4e-12 -2.152
HMC_vs_DEMetro_Z 3 -13.735 3.18e-14 -2.508
HMC_vs_DEMetro_Z 4 -20.790 5.73e-19 -3.796
HMC_vs_Metro 0 1.642 0.111 0.300
HMC_vs_Metro 1 0.893 0.379 0.163
HMC_vs_Metro 2 2.129 0.0419 0.389
HMC_vs_Metro 3 2.850 0.00797 0.520
HMC_vs_Metro 4 1.886 0.0694 0.344
HMC_vs_SMC 0 80.535 1.18e-35 14.704
HMC_vs_SMC 1 61.095 3.39e-32 11.154
HMC_vs_SMC 2 80.592 1.15e-35 14.714
HMC_vs_SMC 3 82.515 5.84e-36 15.065
HMC_vs_SMC 4 132.386 6.73e-42 24.170
Metro_vs_SMC 0 33.024 1.46e-24 6.029
Metro_vs_SMC 1 19.851 2.01e-18 3.624
Metro_vs_SMC 2 20.169 1.31e-18 3.682
Metro_vs_SMC 3 19.778 2.22e-18 3.611
Metro_vs_SMC 4 24.448 6.67e-21 4.464
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 3.876 0.090 0.045 83.686
HMC 5 2.212 0.066 0.031 69.323
HMC 10 1.581 0.050 0.013 117.814
HMC 15 1.255 0.047 0.013 94.223
HMC 30 0.884 0.037 0.004 193.248
SMC 2 0.098 0.090 0.045 0.183
SMC 5 0.057 0.066 0.031 -0.315
SMC 10 0.050 0.050 0.013 -0.022
SMC 15 0.046 0.047 0.013 -0.086
SMC 30 0.037 0.037 0.004 0.132
Metro 2 3.687 0.090 0.045 79.522
Metro 5 2.107 0.066 0.031 65.918
Metro 10 1.442 0.050 0.013 107.118
Metro 15 1.098 0.047 0.013 82.015
Metro 30 0.824 0.037 0.004 179.603
DEMetro_Z 2 3.454 0.090 0.045 74.369
DEMetro_Z 5 2.556 0.066 0.031 80.421
DEMetro_Z 10 5.817 0.050 0.013 443.844
DEMetro_Z 15 8.033 0.047 0.013 623.115
DEMetro_Z 30 9.168 0.037 0.004 2082.460
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2 154.155 8.38e-53 83.253
HMC 5 175.174 2.96e-63 70.225
HMC 10 165.744 1.09e-50 109.890
HMC 15 144.151 1.21e-47 104.856
HMC 30 149.223 8.15e-45 195.475
SMC 2 0.921 0.361 0.253
SMC 5 -1.407 0.165 -0.332
SMC 10 -0.329 0.743 -0.092
SMC 15 0.146 0.885 0.040
SMC 30 0.415 0.679 0.121
Metro 2 37.714 1.81e-26 80.674
Metro 5 20.853 4.37e-19 64.492
Metro 10 21.675 1.68e-19 100.302
Metro 15 20.293 1.02e-18 92.933
Metro 30 24.543 5.76e-21 180.596
DEMetro_Z 2 17.256 7.94e-17 74.880
DEMetro_Z 5 39.620 2.7e-27 64.488
DEMetro_Z 10 38.576 1.5e-26 158.916
DEMetro_Z 15 55.153 4.55e-31 177.798
DEMetro_Z 30 58.180 1.28e-31 406.805
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 17.293 8.12e-17 3.157
DEMetro_Z_vs_SMC 1 39.828 7.17e-27 7.272
DEMetro_Z_vs_SMC 2 38.982 1.32e-26 7.117
DEMetro_Z_vs_SMC 3 55.722 4.79e-31 10.173
DEMetro_Z_vs_SMC 4 57.548 1.9e-31 10.507
HMC_vs_Metro 0 1.234 0.227 0.225
HMC_vs_Metro 1 1.899 0.0676 0.347
HMC_vs_Metro 2 2.127 0.0421 0.388
HMC_vs_Metro 3 2.580 0.0152 0.471
HMC_vs_Metro 4 2.003 0.0546 0.366
Metro_vs_DEMetro_Z 0 1.183 0.247 0.216
Metro_vs_DEMetro_Z 1 0.001 0.999 0.000
Metro_vs_DEMetro_Z 2 -9.342 3.02e-10 -1.706
Metro_vs_DEMetro_Z 3 -18.563 1.23e-17 -3.389
Metro_vs_DEMetro_Z 4 -23.093 3.22e-20 -4.216
HMC_vs_SMC 0 162.155 1.89e-44 29.605
HMC_vs_SMC 1 177.635 1.35e-45 32.432
HMC_vs_SMC 2 186.273 3.41e-46 34.009
HMC_vs_SMC 3 152.150 1.2e-43 27.779
HMC_vs_SMC 4 147.351 3.03e-43 26.903
Metro_vs_SMC 0 37.161 5.16e-26 6.785
Metro_vs_SMC 1 21.112 3.77e-19 3.854
Metro_vs_SMC 2 21.414 2.56e-19 3.910
Metro_vs_SMC 3 20.548 7.88e-19 3.752
Metro_vs_SMC 4 24.376 7.24e-21 4.450
HMC_vs_DEMetro_Z 0 1.858 0.0734 0.339
HMC_vs_DEMetro_Z 1 3.453 0.00173 0.630
HMC_vs_DEMetro_Z 2 -11.591 2.1e-12 -2.116
HMC_vs_DEMetro_Z 3 -22.875 4.19e-20 -4.176
HMC_vs_DEMetro_Z 4 -31.878 3.97e-24 -5.820
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2 0.617 0.012 0.007 83.253
HMC 5 0.598 0.014 0.008 70.225
HMC 10 0.567 0.014 0.005 109.890
HMC 15 0.537 0.014 0.005 104.856
HMC 30 0.457 0.013 0.002 195.475
SMC 2 0.014 0.012 0.007 0.253
SMC 5 0.012 0.014 0.008 -0.332
SMC 10 0.013 0.014 0.005 -0.092
SMC 15 0.015 0.014 0.005 0.040
SMC 30 0.013 0.013 0.002 0.121
Metro 2 0.599 0.012 0.007 80.674
Metro 5 0.550 0.014 0.008 64.492
Metro 10 0.518 0.014 0.005 100.302
Metro 15 0.477 0.014 0.005 92.933
Metro 30 0.423 0.013 0.002 180.596
DEMetro_Z 2 0.557 0.012 0.007 74.880
DEMetro_Z 5 0.550 0.014 0.008 64.488
DEMetro_Z 10 0.813 0.014 0.005 158.916
DEMetro_Z 15 0.900 0.014 0.005 177.798
DEMetro_Z 30 0.937 0.013 0.002 406.805
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
Trace Plots
Pooled
2 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
30 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
30 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2
5
10
15
30
Chain
2
5
10
15
30

two_attr_mm

▼

Varying_Mode_Distance_with_high_Dimension (Mixture, mm, 30 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 4.711 5.13e-05 5.703
HMC 8 7.325 4.5e-08 43.075
HMC 10 5.657 4.08e-06 37.840
HMC 12 4.511 9.83e-05 35.092
HMC 15 5.868 2.27e-06 32.457
HMC 18 5.652 4.13e-06 35.073
SMC 5 1.317 0.193 0.367
SMC 8 1.839 0.0712 0.527
SMC 10 1.480 0.145 0.431
SMC 12 0.792 0.431 0.217
SMC 15 1.656 0.103 0.480
SMC 18 1.109 0.272 0.271
Metro 5 11.035 9.89e-13 7.333
Metro 8 7.117 7.46e-08 19.574
Metro 10 6.954 1.2e-07 43.789
Metro 12 5.660 4.05e-06 39.588
Metro 15 5.915 2e-06 34.675
Metro 18 5.811 2.66e-06 35.599
DEMetro_Z 5 30.134 1.94e-23 2136.801
DEMetro_Z 8 48.601 2.41e-29 1287.729
DEMetro_Z 10 37.849 3.05e-26 962.075
DEMetro_Z 12 42.889 8.59e-28 767.635
DEMetro_Z 15 52.677 2.3e-30 474.497
DEMetro_Z 18 46.573 7.86e-29 399.933
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -30.032 2.13e-23 -5.483
HMC_vs_DEMetro_Z 1 -46.420 9.03e-29 -8.475
HMC_vs_DEMetro_Z 2 -36.830 6.65e-26 -6.724
HMC_vs_DEMetro_Z 3 -40.202 5.5e-27 -7.340
HMC_vs_DEMetro_Z 4 -39.845 7.09e-27 -7.275
HMC_vs_DEMetro_Z 5 -41.312 2.53e-27 -7.542
Metro_vs_SMC 0 10.297 3.38e-11 1.880
Metro_vs_SMC 1 6.837 1.65e-07 1.248
Metro_vs_SMC 2 6.811 1.77e-07 1.244
Metro_vs_SMC 3 5.623 4.5e-06 1.027
Metro_vs_SMC 4 5.860 2.34e-06 1.070
Metro_vs_SMC 5 5.829 2.55e-06 1.064
Metro_vs_DEMetro_Z 0 -30.014 2.17e-23 -5.480
Metro_vs_DEMetro_Z 1 -48.052 3.36e-29 -8.773
Metro_vs_DEMetro_Z 2 -34.510 4.21e-25 -6.301
Metro_vs_DEMetro_Z 3 -39.706 7.83e-27 -7.249
Metro_vs_DEMetro_Z 4 -38.386 2.05e-26 -7.008
Metro_vs_DEMetro_Z 5 -41.423 2.34e-27 -7.563
HMC_vs_Metro 0 -1.191 0.243 -0.218
HMC_vs_Metro 1 3.288 0.00265 0.600
HMC_vs_Metro 2 -0.697 0.491 -0.127
HMC_vs_Metro 3 -0.848 0.403 -0.155
HMC_vs_Metro 4 -1.313 0.2 -0.240
HMC_vs_Metro 5 -4.696 5.91e-05 -0.857
HMC_vs_SMC 0 4.450 0.000117 0.812
HMC_vs_SMC 1 7.208 6.18e-08 1.316
HMC_vs_SMC 2 5.567 5.25e-06 1.016
HMC_vs_SMC 3 4.468 0.000111 0.816
HMC_vs_SMC 4 5.808 2.7e-06 1.060
HMC_vs_SMC 5 5.667 3.98e-06 1.035
DEMetro_Z_vs_SMC 0 30.123 1.96e-23 5.500
DEMetro_Z_vs_SMC 1 48.715 2.27e-29 8.894
DEMetro_Z_vs_SMC 2 37.796 3.19e-26 6.901
DEMetro_Z_vs_SMC 3 42.939 8.39e-28 7.840
DEMetro_Z_vs_SMC 4 52.548 2.58e-30 9.594
DEMetro_Z_vs_SMC 5 46.915 6.67e-29 8.565
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.041 0.024 0.003 5.703
HMC 8 0.254 0.026 0.005 43.075
HMC 10 0.290 0.029 0.007 37.840
HMC 12 0.324 0.030 0.008 35.092
HMC 15 0.469 0.035 0.013 32.457
HMC 18 0.608 0.038 0.016 35.073
SMC 5 0.025 0.024 0.003 0.367
SMC 8 0.029 0.026 0.005 0.527
SMC 10 0.032 0.029 0.007 0.431
SMC 12 0.032 0.030 0.008 0.217
SMC 15 0.041 0.035 0.013 0.480
SMC 18 0.042 0.038 0.016 0.271
Metro 5 0.046 0.024 0.003 7.333
Metro 8 0.130 0.026 0.005 19.574
Metro 10 0.331 0.029 0.007 43.789
Metro 12 0.362 0.030 0.008 39.588
Metro 15 0.499 0.035 0.013 34.675
Metro 18 0.616 0.038 0.016 35.599
DEMetro_Z 5 6.491 0.024 0.003 2136.801
DEMetro_Z 8 6.846 0.026 0.005 1287.729
DEMetro_Z 10 6.663 0.029 0.007 962.075
DEMetro_Z 12 6.473 0.030 0.008 767.635
DEMetro_Z 15 6.389 0.035 0.013 474.497
DEMetro_Z 18 6.536 0.038 0.016 399.933
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 3.285 0.00185 0.724
HMC 8 4.459 0.000114 34.579
HMC 10 4.454 0.000115 29.993
HMC 12 3.487 0.00158 43.620
HMC 15 4.368 0.000146 87.346
HMC 18 4.240 0.000208 143.291
SMC 5 3.757 0.000407 1.047
SMC 8 2.097 0.0404 0.534
SMC 10 2.670 0.00987 0.646
SMC 12 1.840 0.071 0.504
SMC 15 1.322 0.193 0.513
SMC 18 3.912 0.000348 1.775
Metro 5 8.952 2.34e-12 2.607
Metro 8 5.384 8e-06 8.232
Metro 10 4.039 0.000359 34.661
Metro 12 3.887 0.000543 43.817
Metro 15 4.259 0.000197 98.969
Metro 18 4.288 0.000182 144.690
DEMetro_Z 5 41.113 2.9e-27 18548.245
DEMetro_Z 8 37.363 4.42e-26 12570.720
DEMetro_Z 10 44.722 2.62e-28 7070.777
DEMetro_Z 12 36.297 1.01e-25 5917.856
DEMetro_Z 15 30.907 9.5e-24 6963.578
DEMetro_Z 18 31.575 5.2e-24 6662.214
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -1.558 0.13 -0.284
HMC_vs_SMC 1 4.398 0.000134 0.803
HMC_vs_SMC 2 4.377 0.000142 0.799
HMC_vs_SMC 3 3.445 0.00176 0.629
HMC_vs_SMC 4 4.330 0.000162 0.791
HMC_vs_SMC 5 4.191 0.000238 0.765
Metro_vs_DEMetro_Z 0 -41.113 2.9e-27 -7.506
Metro_vs_DEMetro_Z 1 -37.318 4.58e-26 -6.813
Metro_vs_DEMetro_Z 2 -43.651 5.25e-28 -7.970
Metro_vs_DEMetro_Z 3 -35.415 2.02e-25 -6.466
Metro_vs_DEMetro_Z 4 -29.641 3.08e-23 -5.412
Metro_vs_DEMetro_Z 5 -30.026 2.15e-23 -5.482
HMC_vs_Metro 0 -8.615 1.73e-09 -1.573
HMC_vs_Metro 1 3.237 0.00302 0.591
HMC_vs_Metro 2 -0.431 0.67 -0.079
HMC_vs_Metro 3 -0.021 0.983 -0.004
HMC_vs_Metro 4 -1.050 0.302 -0.192
HMC_vs_Metro 5 -2.587 0.015 -0.472
HMC_vs_DEMetro_Z 0 -41.114 2.9e-27 -7.506
HMC_vs_DEMetro_Z 1 -37.657 3.54e-26 -6.875
HMC_vs_DEMetro_Z 2 -44.812 2.48e-28 -8.182
HMC_vs_DEMetro_Z 3 -35.544 1.82e-25 -6.489
HMC_vs_DEMetro_Z 4 -29.857 2.51e-23 -5.451
HMC_vs_DEMetro_Z 5 -30.038 2.12e-23 -5.484
Metro_vs_SMC 0 4.547 8.91e-05 0.830
Metro_vs_SMC 1 5.065 2.12e-05 0.925
Metro_vs_SMC 2 3.963 0.000442 0.724
Metro_vs_SMC 3 3.838 0.00062 0.701
Metro_vs_SMC 4 4.237 0.000209 0.774
Metro_vs_SMC 5 4.239 0.000208 0.774
DEMetro_Z_vs_SMC 0 41.112 2.9e-27 7.506
DEMetro_Z_vs_SMC 1 37.365 4.42e-26 6.822
DEMetro_Z_vs_SMC 2 44.712 2.64e-28 8.163
DEMetro_Z_vs_SMC 3 36.294 1.01e-25 6.626
DEMetro_Z_vs_SMC 4 30.902 9.54e-24 5.642
DEMetro_Z_vs_SMC 5 31.551 5.31e-24 5.760
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.044 0.037 0.009 0.724
HMC 8 0.510 0.044 0.013 34.579
HMC 10 0.787 0.053 0.024 29.993
HMC 12 1.293 0.056 0.028 43.620
HMC 15 2.082 0.058 0.023 87.346
HMC 18 3.716 0.055 0.026 143.291
SMC 5 0.047 0.037 0.009 1.047
SMC 8 0.051 0.044 0.013 0.534
SMC 10 0.069 0.053 0.024 0.646
SMC 12 0.070 0.056 0.028 0.504
SMC 15 0.070 0.058 0.023 0.513
SMC 18 0.101 0.055 0.026 1.775
Metro 5 0.062 0.037 0.009 2.607
Metro 8 0.155 0.044 0.013 8.232
Metro 10 0.902 0.053 0.024 34.661
Metro 12 1.299 0.056 0.028 43.817
Metro 15 2.352 0.058 0.023 98.969
Metro 18 3.752 0.055 0.026 144.690
DEMetro_Z 5 174.763 0.037 0.009 18548.245
DEMetro_Z 8 169.335 0.044 0.013 12570.720
DEMetro_Z 10 173.254 0.053 0.024 7070.777
DEMetro_Z 12 167.964 0.056 0.028 5917.856
DEMetro_Z 15 161.454 0.058 0.023 6963.578
DEMetro_Z 18 170.256 0.055 0.026 6662.214
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 5.194 1.33e-05 6.844
HMC 8 7.202 6.25e-08 55.908
HMC 10 5.745 3.2e-06 46.885
HMC 12 4.521 9.56e-05 43.844
HMC 15 5.888 2.16e-06 40.602
HMC 18 5.713 3.5e-06 41.869
SMC 5 2.506 0.0151 0.668
SMC 8 2.693 0.00938 0.800
SMC 10 2.047 0.0455 0.595
SMC 12 1.383 0.172 0.388
SMC 15 2.111 0.0394 0.634
SMC 18 1.514 0.136 0.374
Metro 5 12.315 7.44e-14 9.002
Metro 8 7.078 8.46e-08 25.662
Metro 10 6.851 1.58e-07 52.590
Metro 12 5.580 5.05e-06 50.843
Metro 15 5.985 1.65e-06 42.794
Metro 18 5.893 2.13e-06 42.607
DEMetro_Z 5 59.731 6.49e-32 5564.953
DEMetro_Z 8 71.796 3.23e-34 3272.028
DEMetro_Z 10 68.698 1.15e-33 2292.047
DEMetro_Z 12 65.551 4.45e-33 1905.649
DEMetro_Z 15 60.502 4.44e-32 1109.462
DEMetro_Z 18 57.260 2.16e-31 894.223
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -59.633 6.81e-32 -10.887
Metro_vs_DEMetro_Z 1 -71.250 4.04e-34 -13.008
Metro_vs_DEMetro_Z 2 -61.312 3.06e-32 -11.194
Metro_vs_DEMetro_Z 3 -59.302 7.99e-32 -10.827
Metro_vs_DEMetro_Z 4 -48.594 2.44e-29 -8.872
Metro_vs_DEMetro_Z 5 -56.316 3.53e-31 -10.282
DEMetro_Z_vs_SMC 0 59.703 6.59e-32 10.900
DEMetro_Z_vs_SMC 1 71.777 3.27e-34 13.105
DEMetro_Z_vs_SMC 2 68.771 1.12e-33 12.556
DEMetro_Z_vs_SMC 3 65.577 4.42e-33 11.973
DEMetro_Z_vs_SMC 4 60.593 4.3e-32 11.063
DEMetro_Z_vs_SMC 5 57.405 2.04e-31 10.481
HMC_vs_DEMetro_Z 0 -59.673 6.68e-32 -10.895
HMC_vs_DEMetro_Z 1 -72.999 2.01e-34 -13.328
HMC_vs_DEMetro_Z 2 -68.703 1.15e-33 -12.543
HMC_vs_DEMetro_Z 3 -60.868 3.78e-32 -11.113
HMC_vs_DEMetro_Z 4 -49.163 1.74e-29 -8.976
HMC_vs_DEMetro_Z 5 -56.482 3.25e-31 -10.312
HMC_vs_Metro 0 -1.420 0.166 -0.259
HMC_vs_Metro 1 3.197 0.00335 0.584
HMC_vs_Metro 2 -0.555 0.583 -0.101
HMC_vs_Metro 3 -1.038 0.308 -0.189
HMC_vs_Metro 4 -1.085 0.287 -0.198
HMC_vs_Metro 5 -1.246 0.223 -0.228
HMC_vs_SMC 0 4.745 5.16e-05 0.866
HMC_vs_SMC 1 7.069 8.92e-08 1.291
HMC_vs_SMC 2 5.641 4.29e-06 1.030
HMC_vs_SMC 3 4.464 0.000112 0.815
HMC_vs_SMC 4 5.813 2.66e-06 1.061
HMC_vs_SMC 5 5.702 3.62e-06 1.041
Metro_vs_SMC 0 11.210 4.65e-12 2.047
Metro_vs_SMC 1 6.791 1.87e-07 1.240
Metro_vs_SMC 2 6.726 2.22e-07 1.228
Metro_vs_SMC 3 5.527 5.87e-06 1.009
Metro_vs_SMC 4 5.916 2.01e-06 1.080
Metro_vs_SMC 5 5.888 2.17e-06 1.075
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.044 0.031 0.002 6.844
HMC 8 0.206 0.033 0.003 55.908
HMC 10 0.243 0.036 0.004 46.885
HMC 12 0.264 0.037 0.005 43.844
HMC 15 0.391 0.042 0.009 40.602
HMC 18 0.497 0.045 0.011 41.869
SMC 5 0.032 0.031 0.002 0.668
SMC 8 0.036 0.033 0.003 0.800
SMC 10 0.039 0.036 0.004 0.595
SMC 12 0.039 0.037 0.005 0.388
SMC 15 0.047 0.042 0.009 0.634
SMC 18 0.049 0.045 0.011 0.374
Metro 5 0.048 0.031 0.002 9.002
Metro 8 0.112 0.033 0.003 25.662
Metro 10 0.268 0.036 0.004 52.590
Metro 12 0.301 0.037 0.005 50.843
Metro 15 0.410 0.042 0.009 42.794
Metro 18 0.504 0.045 0.011 42.607
DEMetro_Z 5 10.220 0.031 0.002 5564.953
DEMetro_Z 8 10.123 0.033 0.003 3272.028
DEMetro_Z 10 10.144 0.036 0.004 2292.047
DEMetro_Z 12 9.907 0.037 0.005 1905.649
DEMetro_Z 15 9.590 0.042 0.009 1109.462
DEMetro_Z 18 9.686 0.045 0.011 894.223
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 5.085 1.76e-05 5.833
HMC 8 7.355 4.17e-08 47.155
HMC 10 5.573 5.15e-06 44.219
HMC 12 4.506 9.98e-05 41.267
HMC 15 5.824 2.57e-06 38.491
HMC 18 5.706 3.57e-06 41.151
SMC 5 2.902 0.00527 0.697
SMC 8 3.185 0.00233 0.834
SMC 10 2.560 0.0133 0.764
SMC 12 1.488 0.142 0.386
SMC 15 2.239 0.0292 0.655
SMC 18 1.901 0.0623 0.491
Metro 5 11.958 7.57e-14 7.308
Metro 8 7.228 5.6e-08 21.280
Metro 10 6.696 2.39e-07 50.438
Metro 12 5.624 4.47e-06 46.542
Metro 15 5.859 2.34e-06 40.942
Metro 18 5.831 2.52e-06 41.959
DEMetro_Z 5 84.681 2.19e-36 369.241
DEMetro_Z 8 90.278 2.49e-37 257.356
DEMetro_Z 10 91.553 1.31e-37 219.735
DEMetro_Z 12 93.712 4.86e-38 191.061
DEMetro_Z 15 112.448 2.11e-41 133.388
DEMetro_Z 18 77.700 5.58e-36 120.454
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 84.834 2.62e-36 15.489
DEMetro_Z_vs_SMC 1 90.789 3.69e-37 16.576
DEMetro_Z_vs_SMC 2 87.293 1.15e-36 15.937
DEMetro_Z_vs_SMC 3 92.133 2.41e-37 16.821
DEMetro_Z_vs_SMC 4 106.238 3.93e-39 19.396
DEMetro_Z_vs_SMC 5 78.639 2.34e-35 14.357
HMC_vs_Metro 0 -1.132 0.267 -0.207
HMC_vs_Metro 1 3.355 0.00223 0.612
HMC_vs_Metro 2 -0.610 0.547 -0.111
HMC_vs_Metro 3 -0.815 0.422 -0.149
HMC_vs_Metro 4 -1.117 0.273 -0.204
HMC_vs_Metro 5 -1.755 0.0898 -0.320
Metro_vs_DEMetro_Z 0 -77.707 3.31e-35 -14.187
Metro_vs_DEMetro_Z 1 -56.403 3.38e-31 -10.298
Metro_vs_DEMetro_Z 2 -20.711 6.36e-19 -3.781
Metro_vs_DEMetro_Z 3 -17.127 1.05e-16 -3.127
Metro_vs_DEMetro_Z 4 -13.770 2.99e-14 -2.514
Metro_vs_DEMetro_Z 5 -11.726 1.58e-12 -2.141
HMC_vs_SMC 0 4.452 0.000116 0.813
HMC_vs_SMC 1 7.221 5.97e-08 1.318
HMC_vs_SMC 2 5.457 7.13e-06 0.996
HMC_vs_SMC 3 4.450 0.000116 0.813
HMC_vs_SMC 4 5.743 3.23e-06 1.048
HMC_vs_SMC 5 5.682 3.82e-06 1.037
Metro_vs_SMC 0 10.867 9.68e-12 1.984
Metro_vs_SMC 1 6.894 1.42e-07 1.259
Metro_vs_SMC 2 6.546 3.6e-07 1.195
Metro_vs_SMC 3 5.572 5.19e-06 1.017
Metro_vs_SMC 4 5.789 2.84e-06 1.057
Metro_vs_SMC 5 5.809 2.69e-06 1.061
HMC_vs_DEMetro_Z 0 -77.089 4.16e-35 -14.074
HMC_vs_DEMetro_Z 1 -27.438 2.69e-22 -5.009
HMC_vs_DEMetro_Z 2 -19.969 1.71e-18 -3.646
HMC_vs_DEMetro_Z 3 -16.132 5.07e-16 -2.945
HMC_vs_DEMetro_Z 4 -15.125 2.71e-15 -2.761
HMC_vs_DEMetro_Z 5 -11.801 1.36e-12 -2.155
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.023 0.014 0.002 5.833
HMC 8 0.117 0.013 0.002 47.155
HMC 10 0.127 0.014 0.003 44.219
HMC 12 0.133 0.013 0.003 41.267
HMC 15 0.174 0.013 0.004 38.491
HMC 18 0.202 0.012 0.005 41.151
SMC 5 0.015 0.014 0.002 0.697
SMC 8 0.015 0.013 0.002 0.834
SMC 10 0.016 0.014 0.003 0.764
SMC 12 0.014 0.013 0.003 0.386
SMC 15 0.016 0.013 0.004 0.655
SMC 18 0.015 0.012 0.005 0.491
Metro 5 0.025 0.014 0.002 7.308
Metro 8 0.060 0.013 0.002 21.280
Metro 10 0.143 0.014 0.003 50.438
Metro 12 0.149 0.013 0.003 46.542
Metro 15 0.184 0.013 0.004 40.942
Metro 18 0.206 0.012 0.005 41.959
DEMetro_Z 5 0.575 0.014 0.002 369.241
DEMetro_Z 8 0.578 0.013 0.002 257.356
DEMetro_Z 10 0.577 0.014 0.003 219.735
DEMetro_Z 12 0.569 0.013 0.003 191.061
DEMetro_Z 15 0.569 0.013 0.004 133.388
DEMetro_Z 18 0.568 0.012 0.005 120.454
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 3.810 0.000619 3.907
HMC 8 8.192 4.92e-09 78.034
HMC 10 261.345 1.35e-63 128.165
HMC 12 279.061 3.06e-67 126.233
HMC 15 287.198 1.13e-79 99.938
HMC 18 276.741 2.04e-77 98.958
SMC 5 0.055 0.956 0.014
SMC 8 0.995 0.324 0.294
SMC 10 0.943 0.35 0.333
SMC 12 0.316 0.753 0.083
SMC 15 0.282 0.779 0.082
SMC 18 -0.577 0.567 -0.141
Metro 5 9.892 1.8e-11 6.703
Metro 8 6.390 5.35e-07 21.036
Metro 10 9.382 2.72e-10 72.946
Metro 12 16.670 2.07e-16 109.305
Metro 15 39.615 5.12e-27 97.488
Metro 18 279.447 5e-78 99.165
DEMetro_Z 5 21.502 2.29e-19 3443.156
DEMetro_Z 8 23.698 1.58e-20 2122.739
DEMetro_Z 10 22.445 7.05e-20 1644.831
DEMetro_Z 12 22.792 4.62e-20 1358.805
DEMetro_Z 15 25.249 2.72e-21 889.869
DEMetro_Z 18 24.064 1.03e-20 650.555
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -21.427 2.52e-19 -3.912
HMC_vs_DEMetro_Z 1 -22.816 4.49e-20 -4.166
HMC_vs_DEMetro_Z 2 -20.702 6.44e-19 -3.780
HMC_vs_DEMetro_Z 3 -20.618 7.19e-19 -3.764
HMC_vs_DEMetro_Z 4 -22.478 6.77e-20 -4.104
HMC_vs_DEMetro_Z 5 -20.411 9.45e-19 -3.727
Metro_vs_SMC 0 9.805 1.03e-10 1.790
Metro_vs_SMC 1 6.243 8.2e-07 1.140
Metro_vs_SMC 2 9.410 2.58e-10 1.718
Metro_vs_SMC 3 16.759 1.86e-16 3.060
Metro_vs_SMC 4 40.311 5.09e-27 7.360
Metro_vs_SMC 5 319.992 5.26e-53 58.422
Metro_vs_DEMetro_Z 0 -21.478 2.36e-19 -3.921
Metro_vs_DEMetro_Z 1 -23.200 2.84e-20 -4.236
Metro_vs_DEMetro_Z 2 -21.939 1.32e-19 -4.005
Metro_vs_DEMetro_Z 3 -20.581 7.54e-19 -3.758
Metro_vs_DEMetro_Z 4 -22.391 7.53e-20 -4.088
Metro_vs_DEMetro_Z 5 -20.410 9.47e-19 -3.726
HMC_vs_Metro 0 -2.369 0.0247 -0.432
HMC_vs_Metro 1 5.704 3.6e-06 1.041
HMC_vs_Metro 2 7.077 8.72e-08 1.292
HMC_vs_Metro 3 2.563 0.0158 0.468
HMC_vs_Metro 4 1.013 0.319 0.185
HMC_vs_Metro 5 -2.072 0.0473 -0.378
HMC_vs_SMC 0 3.943 0.000467 0.720
HMC_vs_SMC 1 8.127 5.82e-09 1.484
HMC_vs_SMC 2 214.572 5.65e-48 39.175
HMC_vs_SMC 3 264.928 1.25e-50 48.369
HMC_vs_SMC 4 457.315 1.68e-57 83.494
HMC_vs_SMC 5 320.388 5.08e-53 58.494
DEMetro_Z_vs_SMC 0 21.507 2.27e-19 3.927
DEMetro_Z_vs_SMC 1 23.685 1.6e-20 4.324
DEMetro_Z_vs_SMC 2 22.438 7.11e-20 4.097
DEMetro_Z_vs_SMC 3 22.798 4.59e-20 4.162
DEMetro_Z_vs_SMC 4 25.300 2.58e-21 4.619
DEMetro_Z_vs_SMC 5 24.036 1.07e-20 4.388
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.036 0.024 0.003 3.907
HMC 8 0.439 0.026 0.005 78.034
HMC 10 0.913 0.029 0.007 128.165
HMC 12 1.089 0.030 0.008 126.233
HMC 15 1.373 0.035 0.013 99.938
HMC 18 1.646 0.038 0.016 98.958
SMC 5 0.024 0.024 0.003 0.014
SMC 8 0.028 0.026 0.005 0.294
SMC 10 0.032 0.029 0.007 0.333
SMC 12 0.030 0.030 0.008 0.083
SMC 15 0.036 0.035 0.013 0.082
SMC 18 0.036 0.038 0.016 -0.141
Metro 5 0.044 0.024 0.003 6.703
Metro 8 0.137 0.026 0.005 21.036
Metro 10 0.532 0.029 0.007 72.946
Metro 12 0.947 0.030 0.008 109.305
Metro 15 1.340 0.035 0.013 97.488
Metro 18 1.649 0.038 0.016 99.165
DEMetro_Z 5 10.444 0.024 0.003 3443.156
DEMetro_Z 8 11.269 0.026 0.005 2122.739
DEMetro_Z 10 11.371 0.029 0.007 1644.831
DEMetro_Z 12 11.435 0.030 0.008 1358.805
DEMetro_Z 15 11.951 0.035 0.013 889.869
DEMetro_Z 18 10.609 0.038 0.016 650.555
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 4.403 5.24e-05 0.991
HMC 8 6.452 4.64e-07 105.806
HMC 10 601.589 4.06e-104 184.434
HMC 12 850.608 1.1e-119 229.911
HMC 15 1084.496 1.28e-96 440.641
HMC 18 1354.342 6.25e-98 576.282
SMC 5 -0.474 0.637 -0.114
SMC 8 0.103 0.918 0.029
SMC 10 0.487 0.628 0.127
SMC 12 0.859 0.394 0.236
SMC 15 -0.101 0.92 -0.031
SMC 18 2.104 0.0408 0.762
Metro 5 9.854 5.35e-14 2.560
Metro 8 3.844 0.000603 9.846
Metro 10 5.984 1.66e-06 79.346
Metro 12 13.412 5.76e-14 190.311
Metro 15 31.856 3.99e-24 427.137
Metro 18 1407.067 6.22e-101 576.431
DEMetro_Z 5 17.750 4.06e-17 2140.110
DEMetro_Z 8 15.060 3.03e-15 1481.650
DEMetro_Z 10 13.088 1.07e-13 758.951
DEMetro_Z 12 16.910 1.47e-16 699.594
DEMetro_Z 15 19.614 2.78e-18 934.961
DEMetro_Z 18 22.720 5.04e-20 942.511
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 5.906 2.06e-06 1.078
HMC_vs_SMC 1 6.452 4.65e-07 1.178
HMC_vs_SMC 2 767.447 5.07e-64 140.116
HMC_vs_SMC 3 1137.600 5.6e-69 207.696
HMC_vs_SMC 4 1174.550 2.21e-69 214.443
HMC_vs_SMC 5 1170.897 2.42e-69 213.776
Metro_vs_DEMetro_Z 0 -17.725 4.22e-17 -3.236
Metro_vs_DEMetro_Z 1 -14.891 4.05e-15 -2.719
Metro_vs_DEMetro_Z 2 -12.076 7.77e-13 -2.205
Metro_vs_DEMetro_Z 3 -11.671 1.77e-12 -2.131
Metro_vs_DEMetro_Z 4 -10.721 1.33e-11 -1.957
Metro_vs_DEMetro_Z 5 -8.810 1.08e-09 -1.608
HMC_vs_Metro 0 -7.442 3.35e-08 -1.359
HMC_vs_Metro 1 5.948 1.84e-06 1.086
HMC_vs_Metro 2 7.897 1.04e-08 1.442
HMC_vs_Metro 3 2.788 0.00926 0.509
HMC_vs_Metro 4 1.006 0.323 0.184
HMC_vs_Metro 5 -2.050 0.0495 -0.374
HMC_vs_DEMetro_Z 0 -17.743 4.1e-17 -3.239
HMC_vs_DEMetro_Z 1 -14.025 1.88e-14 -2.561
HMC_vs_DEMetro_Z 2 -9.881 8.65e-11 -1.804
HMC_vs_DEMetro_Z 3 -11.348 3.48e-12 -2.072
HMC_vs_DEMetro_Z 4 -10.375 2.85e-11 -1.894
HMC_vs_DEMetro_Z 5 -8.813 1.07e-09 -1.609
Metro_vs_SMC 0 12.808 1.83e-13 2.338
Metro_vs_SMC 1 3.888 0.000542 0.710
Metro_vs_SMC 2 5.991 1.63e-06 1.094
Metro_vs_SMC 3 13.323 6.85e-14 2.433
Metro_vs_SMC 4 31.947 3.74e-24 5.833
Metro_vs_SMC 5 1199.469 1.2e-69 218.992
DEMetro_Z_vs_SMC 0 17.753 4.04e-17 3.241
DEMetro_Z_vs_SMC 1 15.054 3.06e-15 2.749
DEMetro_Z_vs_SMC 2 13.076 1.09e-13 2.387
DEMetro_Z_vs_SMC 3 16.907 1.48e-16 3.087
DEMetro_Z_vs_SMC 4 19.609 2.8e-18 3.580
DEMetro_Z_vs_SMC 5 22.678 5.31e-20 4.140
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.046 0.037 0.009 0.991
HMC 8 1.469 0.044 0.013 105.806
HMC 10 4.571 0.053 0.024 184.434
HMC 12 6.579 0.056 0.028 229.911
HMC 15 10.271 0.058 0.023 440.641
HMC 18 14.778 0.055 0.026 576.282
SMC 5 0.036 0.037 0.009 -0.114
SMC 8 0.044 0.044 0.013 0.029
SMC 10 0.056 0.053 0.024 0.127
SMC 12 0.062 0.056 0.028 0.236
SMC 15 0.057 0.058 0.023 -0.031
SMC 18 0.075 0.055 0.026 0.762
Metro 5 0.061 0.037 0.009 2.560
Metro 8 0.177 0.044 0.013 9.846
Metro 10 1.996 0.053 0.024 79.346
Metro 12 5.455 0.056 0.028 190.311
Metro 15 9.958 0.058 0.023 427.137
Metro 18 14.782 0.055 0.026 576.431
DEMetro_Z 5 20.197 0.037 0.009 2140.110
DEMetro_Z 8 19.998 0.044 0.013 1481.650
DEMetro_Z 10 18.644 0.053 0.024 758.951
DEMetro_Z 12 19.905 0.056 0.028 699.594
DEMetro_Z 15 21.728 0.058 0.023 934.961
DEMetro_Z 18 24.134 0.055 0.026 942.511
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 4.388 0.000126 4.990
HMC 8 8.023 7.54e-09 104.981
HMC 10 109.951 1.32e-40 158.175
HMC 12 103.055 1.37e-39 162.971
HMC 15 115.848 3.93e-42 124.914
HMC 18 116.508 1.87e-42 118.392
SMC 5 -0.158 0.875 -0.038
SMC 8 1.381 0.173 0.407
SMC 10 1.236 0.223 0.446
SMC 12 0.618 0.539 0.169
SMC 15 0.447 0.656 0.133
SMC 18 -0.722 0.474 -0.171
Metro 5 11.058 1.26e-12 7.977
Metro 8 6.236 8.23e-07 27.637
Metro 10 9.209 4.11e-10 89.120
Metro 12 15.772 8.98e-16 138.795
Metro 15 37.782 2.41e-26 119.052
Metro 18 97.239 2.38e-39 121.084
DEMetro_Z 5 21.520 2.23e-19 4749.342
DEMetro_Z 8 24.709 4.97e-21 2998.724
DEMetro_Z 10 23.346 2.39e-20 2137.140
DEMetro_Z 12 23.038 3.44e-20 1832.174
DEMetro_Z 15 25.202 2.87e-21 1149.945
DEMetro_Z 18 25.404 2.3e-21 816.299
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -21.498 2.3e-19 -3.925
Metro_vs_DEMetro_Z 1 -24.154 9.32e-21 -4.410
Metro_vs_DEMetro_Z 2 -22.776 4.71e-20 -4.158
Metro_vs_DEMetro_Z 3 -20.975 4.5e-19 -3.829
Metro_vs_DEMetro_Z 4 -22.614 5.74e-20 -4.129
Metro_vs_DEMetro_Z 5 -21.752 1.67e-19 -3.971
DEMetro_Z_vs_SMC 0 21.522 2.23e-19 3.929
DEMetro_Z_vs_SMC 1 24.703 5e-21 4.510
DEMetro_Z_vs_SMC 2 23.337 2.41e-20 4.261
DEMetro_Z_vs_SMC 3 23.043 3.42e-20 4.207
DEMetro_Z_vs_SMC 4 25.251 2.72e-21 4.610
DEMetro_Z_vs_SMC 5 25.381 2.36e-21 4.634
HMC_vs_DEMetro_Z 0 -21.457 2.42e-19 -3.917
HMC_vs_DEMetro_Z 1 -23.855 1.32e-20 -4.355
HMC_vs_DEMetro_Z 2 -21.538 2.18e-19 -3.932
HMC_vs_DEMetro_Z 3 -20.977 4.49e-19 -3.830
HMC_vs_DEMetro_Z 4 -22.520 6.43e-20 -4.112
HMC_vs_DEMetro_Z 5 -21.482 2.35e-19 -3.922
HMC_vs_Metro 0 -2.253 0.032 -0.411
HMC_vs_Metro 1 5.716 3.48e-06 1.044
HMC_vs_Metro 2 6.971 1.16e-07 1.273
HMC_vs_Metro 3 2.773 0.00961 0.506
HMC_vs_Metro 4 1.907 0.0664 0.348
HMC_vs_Metro 5 -1.913 0.0657 -0.349
HMC_vs_SMC 0 4.504 0.0001 0.822
HMC_vs_SMC 1 7.975 8.54e-09 1.456
HMC_vs_SMC 2 102.581 1.08e-38 18.729
HMC_vs_SMC 3 100.521 1.94e-38 18.353
HMC_vs_SMC 4 126.833 2.33e-41 23.156
HMC_vs_SMC 5 117.652 2.05e-40 21.480
Metro_vs_SMC 0 10.667 1.49e-11 1.948
Metro_vs_SMC 1 6.092 1.24e-06 1.112
Metro_vs_SMC 2 9.213 4.09e-10 1.682
Metro_vs_SMC 3 15.840 8.17e-16 2.892
Metro_vs_SMC 4 38.121 2.5e-26 6.960
Metro_vs_SMC 5 96.392 6.54e-38 17.599
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.040 0.031 0.002 4.990
HMC 8 0.357 0.033 0.003 104.981
HMC 10 0.734 0.036 0.004 158.175
HMC 12 0.881 0.037 0.005 162.971
HMC 15 1.117 0.042 0.009 124.914
HMC 18 1.322 0.045 0.011 118.392
SMC 5 0.031 0.031 0.002 -0.038
SMC 8 0.034 0.033 0.003 0.407
SMC 10 0.038 0.036 0.004 0.446
SMC 12 0.038 0.037 0.005 0.169
SMC 15 0.043 0.042 0.009 0.133
SMC 18 0.043 0.045 0.011 -0.171
Metro 5 0.046 0.031 0.002 7.977
Metro 8 0.118 0.033 0.003 27.637
Metro 10 0.429 0.036 0.004 89.120
Metro 12 0.756 0.037 0.005 138.795
Metro 15 1.066 0.042 0.009 119.052
Metro 18 1.351 0.045 0.011 121.084
DEMetro_Z 5 8.726 0.031 0.002 4749.342
DEMetro_Z 8 9.280 0.033 0.003 2998.724
DEMetro_Z 10 9.461 0.036 0.004 2137.140
DEMetro_Z 12 9.526 0.037 0.005 1832.174
DEMetro_Z 15 9.938 0.042 0.009 1149.945
DEMetro_Z 18 8.846 0.045 0.011 816.299
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 4.316 0.000149 4.092
HMC 8 8.076 6.58e-09 86.224
HMC 10 129.905 2.35e-43 151.738
HMC 12 149.645 7.8e-46 151.356
HMC 15 149.936 1.94e-47 118.681
HMC 18 157.556 7.71e-49 115.430
SMC 5 0.459 0.648 0.116
SMC 8 1.585 0.119 0.479
SMC 10 1.305 0.198 0.470
SMC 12 0.414 0.681 0.111
SMC 15 0.483 0.631 0.144
SMC 18 0.011 0.991 0.003
Metro 5 11.070 6.08e-13 6.694
Metro 8 6.390 5.37e-07 22.818
Metro 10 8.901 8.58e-10 85.186
Metro 12 16.362 3.42e-16 130.843
Metro 15 38.020 1.98e-26 116.536
Metro 18 173.441 3.13e-51 116.105
DEMetro_Z 5 103.321 7.61e-39 597.219
DEMetro_Z 8 58.098 1.35e-31 426.373
DEMetro_Z 10 74.027 1.12e-34 359.262
DEMetro_Z 12 62.775 1.34e-32 319.588
DEMetro_Z 15 48.073 2.87e-29 229.826
DEMetro_Z 18 71.248 2.39e-34 198.777
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 103.114 9.31e-39 18.826
DEMetro_Z_vs_SMC 1 57.482 1.96e-31 10.495
DEMetro_Z_vs_SMC 2 72.712 2.25e-34 13.275
DEMetro_Z_vs_SMC 3 62.236 1.99e-32 11.363
DEMetro_Z_vs_SMC 4 49.634 1.33e-29 9.062
DEMetro_Z_vs_SMC 5 71.448 3.73e-34 13.045
HMC_vs_Metro 0 -2.376 0.0243 -0.434
HMC_vs_Metro 1 5.707 3.57e-06 1.042
HMC_vs_Metro 2 6.961 1.19e-07 1.271
HMC_vs_Metro 3 2.604 0.0144 0.475
HMC_vs_Metro 4 0.738 0.467 0.135
HMC_vs_Metro 5 -0.844 0.406 -0.154
Metro_vs_DEMetro_Z 0 -102.014 1.27e-38 -18.625
Metro_vs_DEMetro_Z 1 -46.583 8.17e-29 -8.505
Metro_vs_DEMetro_Z 2 -26.203 9.71e-22 -4.784
Metro_vs_DEMetro_Z 3 -18.674 1.04e-17 -3.409
Metro_vs_DEMetro_Z 4 -21.188 3.42e-19 -3.868
Metro_vs_DEMetro_Z 5 -28.130 1.34e-22 -5.136
HMC_vs_SMC 0 4.272 0.00019 0.780
HMC_vs_SMC 1 8.004 7.94e-09 1.461
HMC_vs_SMC 2 125.531 3.14e-41 22.919
HMC_vs_SMC 3 147.577 2.9e-43 26.944
HMC_vs_SMC 4 168.237 6.51e-45 30.716
HMC_vs_SMC 5 162.326 1.84e-44 29.637
Metro_vs_SMC 0 10.610 1.69e-11 1.937
Metro_vs_SMC 1 6.196 9.32e-07 1.131
Metro_vs_SMC 2 8.910 8.46e-10 1.627
Metro_vs_SMC 3 16.434 3.12e-16 3.000
Metro_vs_SMC 4 38.667 1.67e-26 7.060
Metro_vs_SMC 5 187.865 2.66e-46 34.299
HMC_vs_DEMetro_Z 0 -96.201 6.93e-38 -17.564
HMC_vs_DEMetro_Z 1 -27.349 2.94e-22 -4.993
HMC_vs_DEMetro_Z 2 -41.982 1.6e-27 -7.665
HMC_vs_DEMetro_Z 3 -32.606 2.1e-24 -5.953
HMC_vs_DEMetro_Z 4 -23.595 1.78e-20 -4.308
HMC_vs_DEMetro_Z 5 -30.278 1.7e-23 -5.528
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.020 0.014 0.002 4.092
HMC 8 0.203 0.013 0.002 86.224
HMC 10 0.402 0.014 0.003 151.738
HMC 12 0.453 0.013 0.003 151.356
HMC 15 0.507 0.013 0.004 118.681
HMC 18 0.544 0.012 0.005 115.430
SMC 5 0.014 0.014 0.002 0.116
SMC 8 0.014 0.013 0.002 0.479
SMC 10 0.015 0.014 0.003 0.470
SMC 12 0.014 0.013 0.003 0.111
SMC 15 0.014 0.013 0.004 0.144
SMC 18 0.012 0.012 0.005 0.003
Metro 5 0.024 0.014 0.002 6.694
Metro 8 0.063 0.013 0.002 22.818
Metro 10 0.232 0.014 0.003 85.186
Metro 12 0.394 0.013 0.003 130.843
Metro 15 0.498 0.013 0.004 116.536
Metro 18 0.548 0.012 0.005 116.105
DEMetro_Z 5 0.921 0.014 0.002 597.219
DEMetro_Z 8 0.949 0.013 0.002 426.373
DEMetro_Z 10 0.934 0.014 0.003 359.262
DEMetro_Z 12 0.942 0.013 0.003 319.588
DEMetro_Z 15 0.970 0.013 0.004 229.826
DEMetro_Z 18 0.929 0.012 0.005 198.777
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
Trace Plots
Pooled
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
8 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
12 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
18 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
8 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
12 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
18 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
5
8
10
12
15
18
Chain
5
8
10
12
15
18

Varying_Mode_Distance_with_high_Correlation (Mixture, mm, 30 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 4.991 2.58e-05 27.386
HMC 8 4.389 0.000137 16.949
HMC 10 6.465 4.4e-07 27.401
HMC 12 6.061 1.33e-06 28.150
HMC 15 7.020 9.96e-08 29.906
HMC 18 6.993 1.05e-07 23.508
SMC 5 -0.169 0.866 -0.053
SMC 8 0.081 0.936 0.023
SMC 10 -0.410 0.684 -0.094
SMC 12 -0.599 0.552 -0.137
SMC 15 1.160 0.251 0.294
SMC 18 -0.223 0.824 -0.057
Metro 5 6.294 7.02e-07 27.919
Metro 8 6.443 4.67e-07 25.877
Metro 10 6.426 4.88e-07 24.374
Metro 12 5.090 1.96e-05 22.125
Metro 15 6.277 7.36e-07 27.919
Metro 18 6.749 2.03e-07 24.612
DEMetro_Z 5 7.699 1.67e-08 27.536
DEMetro_Z 8 6.040 1.4e-06 22.918
DEMetro_Z 10 6.662 2.59e-07 28.554
DEMetro_Z 12 7.387 3.76e-08 27.802
DEMetro_Z 15 6.132 1.09e-06 26.592
DEMetro_Z 18 6.041 1.4e-06 24.393
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -0.025 0.98 -0.005
HMC_vs_DEMetro_Z 1 -1.009 0.321 -0.184
HMC_vs_DEMetro_Z 2 -0.159 0.875 -0.029
HMC_vs_DEMetro_Z 3 0.061 0.952 0.011
HMC_vs_DEMetro_Z 4 0.564 0.577 0.103
HMC_vs_DEMetro_Z 5 -0.199 0.843 -0.036
Metro_vs_SMC 0 6.342 6.25e-07 1.158
Metro_vs_SMC 1 6.361 5.94e-07 1.161
Metro_vs_SMC 2 6.434 4.87e-07 1.175
Metro_vs_SMC 3 5.087 1.99e-05 0.929
Metro_vs_SMC 4 6.140 1.09e-06 1.121
Metro_vs_SMC 5 6.904 1.38e-07 1.260
Metro_vs_DEMetro_Z 0 0.059 0.953 0.011
Metro_vs_DEMetro_Z 1 0.526 0.603 0.096
Metro_vs_DEMetro_Z 2 -0.670 0.508 -0.122
Metro_vs_DEMetro_Z 3 -1.006 0.323 -0.184
Metro_vs_DEMetro_Z 4 0.222 0.826 0.041
Metro_vs_DEMetro_Z 5 0.047 0.963 0.009
HMC_vs_Metro 0 -0.072 0.943 -0.013
HMC_vs_Metro 1 -1.627 0.115 -0.297
HMC_vs_Metro 2 0.517 0.609 0.094
HMC_vs_Metro 3 1.461 0.155 0.267
HMC_vs_Metro 4 0.471 0.641 0.086
HMC_vs_Metro 5 -0.372 0.712 -0.068
HMC_vs_SMC 0 4.940 3e-05 0.902
HMC_vs_SMC 1 4.438 0.00012 0.810
HMC_vs_SMC 2 6.513 3.94e-07 1.189
HMC_vs_SMC 3 6.111 1.18e-06 1.116
HMC_vs_SMC 4 6.841 1.63e-07 1.249
HMC_vs_SMC 5 7.044 9.52e-08 1.286
DEMetro_Z_vs_SMC 0 7.740 1.55e-08 1.413
DEMetro_Z_vs_SMC 1 6.035 1.45e-06 1.102
DEMetro_Z_vs_SMC 2 6.696 2.41e-07 1.222
DEMetro_Z_vs_SMC 3 7.428 3.48e-08 1.356
DEMetro_Z_vs_SMC 4 6.060 1.35e-06 1.106
DEMetro_Z_vs_SMC 5 6.101 1.21e-06 1.114
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.527 0.035 0.018 27.386
HMC 8 0.694 0.057 0.038 16.949
HMC 10 1.437 0.069 0.050 27.401
HMC 12 1.945 0.084 0.066 28.150
HMC 15 2.250 0.081 0.073 29.906
HMC 18 2.259 0.130 0.091 23.508
SMC 5 0.034 0.035 0.018 -0.053
SMC 8 0.058 0.057 0.038 0.023
SMC 10 0.065 0.069 0.050 -0.094
SMC 12 0.075 0.084 0.066 -0.137
SMC 15 0.102 0.081 0.073 0.294
SMC 18 0.124 0.130 0.091 -0.057
Metro 5 0.536 0.035 0.018 27.919
Metro 8 1.030 0.057 0.038 25.877
Metro 10 1.286 0.069 0.050 24.374
Metro 12 1.546 0.084 0.066 22.125
Metro 15 2.106 0.081 0.073 27.919
Metro 18 2.359 0.130 0.091 24.612
DEMetro_Z 5 0.529 0.035 0.018 27.536
DEMetro_Z 8 0.919 0.057 0.038 22.918
DEMetro_Z 10 1.495 0.069 0.050 28.554
DEMetro_Z 12 1.922 0.084 0.066 27.802
DEMetro_Z 15 2.010 0.081 0.073 26.592
DEMetro_Z 18 2.339 0.130 0.091 24.393
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 3.587 0.00121 16.973
HMC 8 3.634 0.00107 20.425
HMC 10 4.642 6.84e-05 43.769
HMC 12 4.829 4.08e-05 80.603
HMC 15 4.833 4.03e-05 64.602
HMC 18 5.413 8.04e-06 59.892
SMC 5 -0.837 0.406 -0.238
SMC 8 -0.203 0.84 -0.054
SMC 10 -0.252 0.802 -0.074
SMC 12 0.825 0.413 0.238
SMC 15 0.286 0.776 0.073
SMC 18 -0.716 0.477 -0.170
Metro 5 4.323 0.000164 17.127
Metro 8 5.262 1.22e-05 33.967
Metro 10 5.117 1.82e-05 36.351
Metro 12 4.345 0.000156 61.776
Metro 15 4.605 7.59e-05 62.105
Metro 18 5.062 2.13e-05 69.930
DEMetro_Z 5 5.617 4.37e-06 12.401
DEMetro_Z 8 4.448 0.000117 26.843
DEMetro_Z 10 4.833 4.02e-05 46.497
DEMetro_Z 12 5.073 2.07e-05 69.218
DEMetro_Z 15 4.574 8.26e-05 56.724
DEMetro_Z 18 4.454 0.000115 73.214
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 3.692 0.000917 0.674
HMC_vs_SMC 1 3.688 0.000926 0.673
HMC_vs_SMC 2 4.625 7.18e-05 0.844
HMC_vs_SMC 3 4.801 4.41e-05 0.877
HMC_vs_SMC 4 4.811 4.29e-05 0.878
HMC_vs_SMC 5 5.413 8.04e-06 0.988
Metro_vs_DEMetro_Z 0 1.010 0.321 0.184
Metro_vs_DEMetro_Z 1 0.784 0.439 0.143
Metro_vs_DEMetro_Z 2 -0.774 0.445 -0.141
Metro_vs_DEMetro_Z 3 -0.385 0.703 -0.070
Metro_vs_DEMetro_Z 4 0.348 0.731 0.063
Metro_vs_DEMetro_Z 5 -0.185 0.854 -0.034
HMC_vs_Metro 0 -0.024 0.981 -0.004
HMC_vs_Metro 1 -1.594 0.122 -0.291
HMC_vs_Metro 2 0.600 0.553 0.110
HMC_vs_Metro 3 1.347 0.188 0.246
HMC_vs_Metro 4 0.189 0.851 0.035
HMC_vs_Metro 5 -1.005 0.323 -0.184
HMC_vs_DEMetro_Z 0 0.967 0.342 0.176
HMC_vs_DEMetro_Z 1 -0.709 0.484 -0.130
HMC_vs_DEMetro_Z 2 -0.174 0.863 -0.032
HMC_vs_DEMetro_Z 3 0.525 0.603 0.096
HMC_vs_DEMetro_Z 4 0.469 0.643 0.086
HMC_vs_DEMetro_Z 5 -0.915 0.368 -0.167
Metro_vs_SMC 0 4.368 0.000146 0.797
Metro_vs_SMC 1 5.241 1.3e-05 0.957
Metro_vs_SMC 2 5.107 1.88e-05 0.932
Metro_vs_SMC 3 4.313 0.00017 0.787
Metro_vs_SMC 4 4.591 7.88e-05 0.838
Metro_vs_SMC 5 5.059 2.15e-05 0.924
DEMetro_Z_vs_SMC 0 5.663 4.03e-06 1.034
DEMetro_Z_vs_SMC 1 4.448 0.000117 0.812
DEMetro_Z_vs_SMC 2 4.824 4.13e-05 0.881
DEMetro_Z_vs_SMC 3 5.033 2.31e-05 0.919
DEMetro_Z_vs_SMC 4 4.589 7.93e-05 0.838
DEMetro_Z_vs_SMC 5 4.458 0.000114 0.814
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.824 0.080 0.044 16.973
HMC 8 1.621 0.103 0.074 20.425
HMC 10 4.819 0.151 0.107 43.769
HMC 12 9.223 0.156 0.112 80.603
HMC 15 11.045 0.219 0.168 64.602
HMC 18 11.045 0.273 0.180 59.892
SMC 5 0.070 0.080 0.044 -0.238
SMC 8 0.099 0.103 0.074 -0.054
SMC 10 0.143 0.151 0.107 -0.074
SMC 12 0.183 0.156 0.112 0.238
SMC 15 0.232 0.219 0.168 0.073
SMC 18 0.242 0.273 0.180 -0.170
Metro 5 0.831 0.080 0.044 17.127
Metro 8 2.628 0.103 0.074 33.967
Metro 10 4.028 0.151 0.107 36.351
Metro 12 7.105 0.156 0.112 61.776
Metro 15 10.626 0.219 0.168 62.105
Metro 18 12.851 0.273 0.180 69.930
DEMetro_Z 5 0.624 0.080 0.044 12.401
DEMetro_Z 8 2.098 0.103 0.074 26.843
DEMetro_Z 10 5.110 0.151 0.107 46.497
DEMetro_Z 12 7.942 0.156 0.112 69.218
DEMetro_Z 15 9.724 0.219 0.168 56.724
DEMetro_Z 18 13.442 0.273 0.180 73.214
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 5.015 2.42e-05 32.795
HMC 8 4.378 0.000141 20.411
HMC 10 6.689 2.41e-07 28.442
HMC 12 5.991 1.61e-06 28.311
HMC 15 7.172 6.67e-08 33.453
HMC 18 6.852 1.54e-07 25.662
SMC 5 -0.794 0.431 -0.236
SMC 8 0.176 0.861 0.050
SMC 10 -0.265 0.792 -0.061
SMC 12 -0.477 0.635 -0.106
SMC 15 1.290 0.202 0.329
SMC 18 -0.578 0.566 -0.146
Metro 5 6.379 5.61e-07 34.298
Metro 8 6.839 1.61e-07 30.274
Metro 10 6.922 1.28e-07 25.467
Metro 12 5.221 1.36e-05 22.052
Metro 15 6.313 6.69e-07 32.605
Metro 18 7.130 7.39e-08 26.602
DEMetro_Z 5 7.873 1.08e-08 32.631
DEMetro_Z 8 6.064 1.32e-06 27.504
DEMetro_Z 10 6.664 2.58e-07 29.261
DEMetro_Z 12 7.382 3.81e-08 27.990
DEMetro_Z 15 6.058 1.35e-06 31.549
DEMetro_Z 18 6.011 1.52e-06 26.324
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 0.220 0.827 0.040
Metro_vs_DEMetro_Z 1 0.433 0.668 0.079
Metro_vs_DEMetro_Z 2 -0.606 0.549 -0.111
Metro_vs_DEMetro_Z 3 -1.070 0.293 -0.195
Metro_vs_DEMetro_Z 4 0.149 0.883 0.027
Metro_vs_DEMetro_Z 5 0.054 0.957 0.010
DEMetro_Z_vs_SMC 0 7.933 9.48e-09 1.448
DEMetro_Z_vs_SMC 1 6.046 1.4e-06 1.104
DEMetro_Z_vs_SMC 2 6.685 2.48e-07 1.220
DEMetro_Z_vs_SMC 3 7.413 3.61e-08 1.353
DEMetro_Z_vs_SMC 4 5.992 1.63e-06 1.094
DEMetro_Z_vs_SMC 5 6.077 1.29e-06 1.110
HMC_vs_DEMetro_Z 0 0.024 0.981 0.004
HMC_vs_DEMetro_Z 1 -1.002 0.324 -0.183
HMC_vs_DEMetro_Z 2 -0.111 0.912 -0.020
HMC_vs_DEMetro_Z 3 0.054 0.957 0.010
HMC_vs_DEMetro_Z 4 0.291 0.773 0.053
HMC_vs_DEMetro_Z 5 -0.135 0.893 -0.025
HMC_vs_Metro 0 -0.167 0.869 -0.030
HMC_vs_Metro 1 -1.550 0.132 -0.283
HMC_vs_Metro 2 0.509 0.615 0.093
HMC_vs_Metro 3 1.448 0.158 0.264
HMC_vs_Metro 4 0.169 0.867 0.031
HMC_vs_Metro 5 -0.278 0.783 -0.051
HMC_vs_SMC 0 5.020 2.4e-05 0.917
HMC_vs_SMC 1 4.427 0.000124 0.808
HMC_vs_SMC 2 6.697 2.4e-07 1.223
HMC_vs_SMC 3 6.024 1.49e-06 1.100
HMC_vs_SMC 4 6.982 1.12e-07 1.275
HMC_vs_SMC 5 6.918 1.33e-07 1.263
Metro_vs_SMC 0 6.445 4.74e-07 1.177
Metro_vs_SMC 1 6.742 2.13e-07 1.231
Metro_vs_SMC 2 6.914 1.35e-07 1.262
Metro_vs_SMC 3 5.203 1.44e-05 0.950
Metro_vs_SMC 4 6.191 9.44e-07 1.130
Metro_vs_SMC 5 7.326 4.54e-08 1.337
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.485 0.048 0.013 32.795
HMC 8 0.662 0.065 0.029 20.411
HMC 10 1.305 0.080 0.043 28.442
HMC 12 1.764 0.093 0.059 28.311
HMC 15 2.005 0.092 0.057 33.453
HMC 18 2.073 0.136 0.075 25.662
SMC 5 0.045 0.048 0.013 -0.236
SMC 8 0.067 0.065 0.029 0.050
SMC 10 0.077 0.080 0.043 -0.061
SMC 12 0.087 0.093 0.059 -0.106
SMC 15 0.110 0.092 0.057 0.329
SMC 18 0.125 0.136 0.075 -0.146
Metro 5 0.505 0.048 0.013 34.298
Metro 8 0.950 0.065 0.029 30.274
Metro 10 1.177 0.080 0.043 25.467
Metro 12 1.394 0.093 0.059 22.052
Metro 15 1.956 0.092 0.057 32.605
Metro 18 2.144 0.136 0.075 26.602
DEMetro_Z 5 0.482 0.048 0.013 32.631
DEMetro_Z 8 0.869 0.065 0.029 27.504
DEMetro_Z 10 1.340 0.080 0.043 29.261
DEMetro_Z 12 1.745 0.093 0.059 27.990
DEMetro_Z 15 1.896 0.092 0.057 31.549
DEMetro_Z 18 2.123 0.136 0.075 26.324
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 4.850 3.83e-05 32.963
HMC 8 4.431 0.000122 19.736
HMC 10 6.661 2.61e-07 31.161
HMC 12 6.158 1.02e-06 33.185
HMC 15 7.255 5.37e-08 35.324
HMC 18 7.119 7.63e-08 28.310
SMC 5 -0.498 0.621 -0.161
SMC 8 0.147 0.883 0.041
SMC 10 -0.642 0.523 -0.144
SMC 12 -0.582 0.563 -0.130
SMC 15 1.303 0.198 0.323
SMC 18 -0.466 0.643 -0.121
Metro 5 6.228 8.44e-07 33.566
Metro 8 6.803 1.78e-07 30.158
Metro 10 6.735 2.12e-07 27.725
Metro 12 5.342 9.71e-06 25.932
Metro 15 6.463 4.45e-07 33.027
Metro 18 7.066 8.79e-08 29.684
DEMetro_Z 5 7.628 2.02e-08 32.467
DEMetro_Z 8 6.026 1.46e-06 26.773
DEMetro_Z 10 6.879 1.45e-07 32.087
DEMetro_Z 12 7.610 2.12e-08 32.924
DEMetro_Z 15 6.312 6.71e-07 31.420
DEMetro_Z 18 6.210 8.85e-07 29.056
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 7.645 1.98e-08 1.396
DEMetro_Z_vs_SMC 1 6.004 1.57e-06 1.096
DEMetro_Z_vs_SMC 2 6.913 1.35e-07 1.262
DEMetro_Z_vs_SMC 3 7.645 1.99e-08 1.396
DEMetro_Z_vs_SMC 4 6.237 8.34e-07 1.139
DEMetro_Z_vs_SMC 5 6.275 7.52e-07 1.146
HMC_vs_Metro 0 -0.065 0.949 -0.012
HMC_vs_Metro 1 -1.682 0.103 -0.307
HMC_vs_Metro 2 0.529 0.601 0.097
HMC_vs_Metro 3 1.534 0.136 0.280
HMC_vs_Metro 4 0.484 0.632 0.088
HMC_vs_Metro 5 -0.392 0.698 -0.072
Metro_vs_DEMetro_Z 0 0.144 0.886 0.026
Metro_vs_DEMetro_Z 1 0.530 0.6 0.097
Metro_vs_DEMetro_Z 2 -0.646 0.523 -0.118
Metro_vs_DEMetro_Z 3 -1.082 0.288 -0.198
Metro_vs_DEMetro_Z 4 0.231 0.819 0.042
Metro_vs_DEMetro_Z 5 0.113 0.911 0.021
HMC_vs_SMC 0 4.842 3.93e-05 0.884
HMC_vs_SMC 1 4.486 0.000106 0.819
HMC_vs_SMC 2 6.696 2.41e-07 1.222
HMC_vs_SMC 3 6.180 9.73e-07 1.128
HMC_vs_SMC 4 7.080 8.66e-08 1.293
HMC_vs_SMC 5 7.173 6.77e-08 1.310
Metro_vs_SMC 0 6.288 7.25e-07 1.148
Metro_vs_SMC 1 6.712 2.3e-07 1.225
Metro_vs_SMC 2 6.761 2.02e-07 1.234
Metro_vs_SMC 3 5.333 1e-05 0.974
Metro_vs_SMC 4 6.335 6.39e-07 1.157
Metro_vs_SMC 5 7.205 6.23e-08 1.315
HMC_vs_DEMetro_Z 0 0.068 0.946 0.012
HMC_vs_DEMetro_Z 1 -1.022 0.315 -0.187
HMC_vs_DEMetro_Z 2 -0.117 0.908 -0.021
HMC_vs_DEMetro_Z 3 0.039 0.969 0.007
HMC_vs_DEMetro_Z 4 0.586 0.563 0.107
HMC_vs_DEMetro_Z 5 -0.140 0.89 -0.026
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.158 0.012 0.004 32.963
HMC 8 0.151 0.012 0.007 19.736
HMC 10 0.261 0.012 0.008 31.161
HMC 12 0.294 0.012 0.008 33.185
HMC 15 0.275 0.010 0.008 35.324
HMC 18 0.236 0.012 0.008 28.310
SMC 5 0.012 0.012 0.004 -0.161
SMC 8 0.012 0.012 0.007 0.041
SMC 10 0.011 0.012 0.008 -0.144
SMC 12 0.011 0.012 0.008 -0.130
SMC 15 0.012 0.010 0.008 0.323
SMC 18 0.012 0.012 0.008 -0.121
Metro 5 0.160 0.012 0.004 33.566
Metro 8 0.225 0.012 0.007 30.158
Metro 10 0.234 0.012 0.008 27.725
Metro 12 0.232 0.012 0.008 25.932
Metro 15 0.258 0.010 0.008 33.027
Metro 18 0.247 0.012 0.008 29.684
DEMetro_Z 5 0.155 0.012 0.004 32.467
DEMetro_Z 8 0.201 0.012 0.007 26.773
DEMetro_Z 10 0.268 0.012 0.008 32.087
DEMetro_Z 12 0.292 0.012 0.008 32.924
DEMetro_Z 15 0.246 0.010 0.008 31.420
DEMetro_Z 18 0.242 0.012 0.008 29.056
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 238.377 1.37e-68 96.579
HMC 8 264.530 1.66e-89 73.843
HMC 10 252.096 7.91e-89 69.309
HMC 12 253.339 1.82e-89 62.836
HMC 15 253.464 8.72e-88 71.980
HMC 18 239.838 4.57e-86 68.719
SMC 5 1.254 0.215 0.387
SMC 8 -0.915 0.364 -0.224
SMC 10 0.135 0.893 0.033
SMC 12 -0.871 0.388 -0.201
SMC 15 1.321 0.192 0.336
SMC 18 -1.196 0.237 -0.289
Metro 5 8.589 1.81e-09 48.019
Metro 8 167.881 2.49e-59 73.751
Metro 10 156.539 7.77e-58 69.372
Metro 12 188.862 3.18e-73 62.704
Metro 15 219.538 3.86e-77 72.016
Metro 18 222.317 4e-80 69.321
DEMetro_Z 5 9.473 2.2e-10 70.133
DEMetro_Z 8 17.039 1.09e-16 66.917
DEMetro_Z 10 17.696 3.89e-17 62.756
DEMetro_Z 12 244.225 4.58e-89 62.752
DEMetro_Z 15 252.674 1.58e-87 72.071
DEMetro_Z 18 250.134 1.07e-88 68.630
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 3.632 0.00108 0.663
HMC_vs_DEMetro_Z 1 1.752 0.0904 0.320
HMC_vs_DEMetro_Z 2 1.877 0.0706 0.343
HMC_vs_DEMetro_Z 3 0.527 0.602 0.096
HMC_vs_DEMetro_Z 4 -0.331 0.743 -0.060
HMC_vs_DEMetro_Z 5 0.382 0.705 0.070
Metro_vs_SMC 0 8.420 2.8e-09 1.537
Metro_vs_SMC 1 156.480 5.31e-44 28.569
Metro_vs_SMC 2 171.414 3.79e-45 31.296
Metro_vs_SMC 3 200.900 3.81e-47 36.679
Metro_vs_SMC 4 207.986 1.4e-47 37.973
Metro_vs_SMC 5 260.440 2.06e-50 47.550
Metro_vs_DEMetro_Z 0 -2.444 0.0208 -0.446
Metro_vs_DEMetro_Z 1 1.721 0.0958 0.314
Metro_vs_DEMetro_Z 2 1.857 0.0735 0.339
Metro_vs_DEMetro_Z 3 -0.233 0.817 -0.043
Metro_vs_DEMetro_Z 4 -0.195 0.847 -0.036
Metro_vs_DEMetro_Z 5 2.752 0.0101 0.502
HMC_vs_Metro 0 8.533 2.12e-09 1.558
HMC_vs_Metro 1 0.192 0.849 0.035
HMC_vs_Metro 2 -0.175 0.862 -0.032
HMC_vs_Metro 3 0.683 0.5 0.125
HMC_vs_Metro 4 -0.158 0.876 -0.029
HMC_vs_Metro 5 -3.076 0.00454 -0.562
HMC_vs_SMC 0 213.653 6.4e-48 39.007
HMC_vs_SMC 1 284.129 1.65e-51 51.875
HMC_vs_SMC 2 242.299 1.67e-49 44.237
HMC_vs_SMC 3 285.437 1.44e-51 52.113
HMC_vs_SMC 4 248.742 7.8e-50 45.414
HMC_vs_SMC 5 226.574 1.17e-48 41.367
DEMetro_Z_vs_SMC 0 9.424 2.49e-10 1.721
DEMetro_Z_vs_SMC 1 17.114 1.07e-16 3.125
DEMetro_Z_vs_SMC 2 17.660 4.65e-17 3.224
DEMetro_Z_vs_SMC 3 251.200 5.87e-50 45.863
DEMetro_Z_vs_SMC 4 231.116 6.57e-49 42.196
DEMetro_Z_vs_SMC 5 265.224 1.21e-50 48.423
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 1.769 0.035 0.018 96.579
HMC 8 2.832 0.057 0.038 73.843
HMC 10 3.529 0.069 0.050 69.309
HMC 12 4.237 0.084 0.066 62.836
HMC 15 5.303 0.081 0.073 71.980
HMC 18 6.353 0.130 0.091 68.719
SMC 5 0.042 0.035 0.018 0.387
SMC 8 0.049 0.057 0.038 -0.224
SMC 10 0.071 0.069 0.050 0.033
SMC 12 0.071 0.084 0.066 -0.201
SMC 15 0.105 0.081 0.073 0.336
SMC 18 0.104 0.130 0.091 -0.289
Metro 5 0.897 0.035 0.018 48.019
Metro 8 2.829 0.057 0.038 73.751
Metro 10 3.532 0.069 0.050 69.372
Metro 12 4.228 0.084 0.066 62.704
Metro 15 5.305 0.081 0.073 72.016
Metro 18 6.407 0.130 0.091 69.321
DEMetro_Z 5 1.294 0.035 0.018 70.133
DEMetro_Z 8 2.572 0.057 0.038 66.917
DEMetro_Z 10 3.202 0.069 0.050 62.756
DEMetro_Z 12 4.231 0.084 0.066 62.752
DEMetro_Z 15 5.309 0.081 0.073 72.071
DEMetro_Z 18 6.345 0.130 0.091 68.630
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 277.842 1.55e-77 99.283
HMC 8 526.307 3.63e-105 150.829
HMC 10 603.284 8.81e-111 164.617
HMC 12 708.821 1.68e-105 224.612
HMC 15 762.698 5.49e-109 235.868
HMC 18 1100.035 9.04e-123 316.837
SMC 5 -0.513 0.61 -0.131
SMC 8 0.909 0.367 0.253
SMC 10 -0.590 0.558 -0.148
SMC 12 -0.010 0.992 -0.003
SMC 15 -0.726 0.471 -0.171
SMC 18 -1.400 0.167 -0.359
Metro 5 5.945 1.84e-06 35.112
Metro 8 418.388 2.3e-85 150.911
Metro 10 550.854 8.16e-104 164.485
Metro 12 661.417 7.45e-99 224.697
Metro 15 718.606 3.67e-103 235.918
Metro 18 1090.493 5.72e-122 316.841
DEMetro_Z 5 8.820 1.04e-09 70.270
DEMetro_Z 8 16.467 2.9e-16 136.131
DEMetro_Z 10 16.398 3.25e-16 148.377
DEMetro_Z 12 704.842 5.89e-105 224.606
DEMetro_Z 15 774.113 1.87e-110 235.774
DEMetro_Z 18 1095.099 2.25e-122 316.770
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 330.485 2.06e-53 60.338
HMC_vs_SMC 1 709.611 4.92e-63 129.557
HMC_vs_SMC 2 856.690 2.09e-65 156.409
HMC_vs_SMC 3 509.166 7.45e-59 92.961
HMC_vs_SMC 4 752.529 8.96e-64 137.392
HMC_vs_SMC 5 927.348 2.1e-66 169.310
Metro_vs_DEMetro_Z 0 -3.546 0.00135 -0.647
Metro_vs_DEMetro_Z 1 1.782 0.0852 0.325
Metro_vs_DEMetro_Z 2 1.788 0.0842 0.326
Metro_vs_DEMetro_Z 3 0.654 0.518 0.119
Metro_vs_DEMetro_Z 4 1.419 0.167 0.259
Metro_vs_DEMetro_Z 5 0.760 0.454 0.139
HMC_vs_Metro 0 11.005 7.2e-12 2.009
HMC_vs_Metro 1 -0.348 0.731 -0.063
HMC_vs_Metro 2 0.737 0.467 0.135
HMC_vs_Metro 3 -0.652 0.519 -0.119
HMC_vs_Metro 4 -0.521 0.606 -0.095
HMC_vs_Metro 5 -0.038 0.97 -0.007
HMC_vs_DEMetro_Z 0 3.661 0.000995 0.668
HMC_vs_DEMetro_Z 1 1.779 0.0857 0.325
HMC_vs_DEMetro_Z 2 1.789 0.084 0.327
HMC_vs_DEMetro_Z 3 0.082 0.935 0.015
HMC_vs_DEMetro_Z 4 1.850 0.0745 0.338
HMC_vs_DEMetro_Z 5 1.705 0.0989 0.311
Metro_vs_SMC 0 5.972 1.72e-06 1.090
Metro_vs_SMC 1 438.457 5.69e-57 80.051
Metro_vs_SMC 2 742.119 1.34e-63 135.492
Metro_vs_SMC 3 505.073 9.41e-59 92.213
Metro_vs_SMC 4 708.823 5.08e-63 129.413
Metro_vs_SMC 5 945.358 1.2e-66 172.598
DEMetro_Z_vs_SMC 0 8.827 1.03e-09 1.612
DEMetro_Z_vs_SMC 1 16.595 2.41e-16 3.030
DEMetro_Z_vs_SMC 2 16.465 2.97e-16 3.006
DEMetro_Z_vs_SMC 3 525.275 3.02e-59 95.902
DEMetro_Z_vs_SMC 4 780.835 3.07e-64 142.560
DEMetro_Z_vs_SMC 5 929.588 1.95e-66 169.719
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 4.434 0.080 0.044 99.283
HMC 8 11.314 0.103 0.074 150.829
HMC 10 17.707 0.151 0.107 164.617
HMC 12 25.421 0.156 0.112 224.612
HMC 15 39.743 0.219 0.168 235.868
HMC 18 57.262 0.273 0.180 316.837
SMC 5 0.074 0.080 0.044 -0.131
SMC 8 0.122 0.103 0.074 0.253
SMC 10 0.136 0.151 0.107 -0.148
SMC 12 0.156 0.156 0.112 -0.003
SMC 15 0.191 0.219 0.168 -0.171
SMC 18 0.208 0.273 0.180 -0.359
Metro 5 1.620 0.080 0.044 35.112
Metro 8 11.320 0.103 0.074 150.911
Metro 10 17.692 0.151 0.107 164.485
Metro 12 25.430 0.156 0.112 224.697
Metro 15 39.752 0.219 0.168 235.918
Metro 18 57.262 0.273 0.180 316.841
DEMetro_Z 5 3.162 0.080 0.044 70.270
DEMetro_Z 8 10.222 0.103 0.074 136.131
DEMetro_Z 10 15.975 0.151 0.107 148.377
DEMetro_Z 12 25.420 0.156 0.112 224.606
DEMetro_Z 15 39.727 0.219 0.168 235.774
DEMetro_Z 18 57.250 0.273 0.180 316.770
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 66.491 7.93e-34 115.359
HMC 8 75.356 2.56e-36 83.801
HMC 10 82.943 1.49e-38 72.939
HMC 12 74.379 2.44e-37 62.082
HMC 15 70.481 2.83e-35 83.012
HMC 18 64.341 3.85e-34 73.946
SMC 5 0.741 0.462 0.225
SMC 8 -0.457 0.649 -0.111
SMC 10 -0.036 0.971 -0.008
SMC 12 -1.046 0.301 -0.232
SMC 15 1.128 0.264 0.300
SMC 18 -1.091 0.28 -0.267
Metro 5 8.403 2.89e-09 58.550
Metro 8 75.370 2.96e-36 85.674
Metro 10 69.685 1.72e-35 72.584
Metro 12 83.303 1.8e-39 63.630
Metro 15 65.150 4.15e-34 81.155
Metro 18 67.841 5.48e-35 74.001
DEMetro_Z 5 9.649 1.46e-10 85.290
DEMetro_Z 8 16.881 1.43e-16 77.330
DEMetro_Z 10 17.317 7.04e-17 65.323
DEMetro_Z 12 94.055 4.83e-42 64.755
DEMetro_Z 15 77.724 7.62e-37 83.351
DEMetro_Z 18 78.783 1.76e-37 74.957
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -2.433 0.0214 -0.444
Metro_vs_DEMetro_Z 1 1.659 0.108 0.303
Metro_vs_DEMetro_Z 2 1.665 0.107 0.304
Metro_vs_DEMetro_Z 3 -1.192 0.243 -0.218
Metro_vs_DEMetro_Z 4 -1.425 0.165 -0.260
Metro_vs_DEMetro_Z 5 -0.621 0.539 -0.113
DEMetro_Z_vs_SMC 0 9.628 1.55e-10 1.758
DEMetro_Z_vs_SMC 1 16.882 1.53e-16 3.082
DEMetro_Z_vs_SMC 2 17.296 8.08e-17 3.158
DEMetro_Z_vs_SMC 3 95.573 8.37e-38 17.449
DEMetro_Z_vs_SMC 4 77.591 3.45e-35 14.166
DEMetro_Z_vs_SMC 5 81.736 7.68e-36 14.923
HMC_vs_DEMetro_Z 0 3.491 0.00156 0.637
HMC_vs_DEMetro_Z 1 1.325 0.196 0.242
HMC_vs_DEMetro_Z 2 1.943 0.0618 0.355
HMC_vs_DEMetro_Z 3 -2.604 0.0144 -0.475
HMC_vs_DEMetro_Z 4 -0.197 0.846 -0.036
HMC_vs_DEMetro_Z 5 -0.671 0.507 -0.123
HMC_vs_Metro 0 7.999 8.03e-09 1.460
HMC_vs_Metro 1 -1.423 0.165 -0.260
HMC_vs_Metro 2 0.247 0.807 0.045
HMC_vs_Metro 3 -1.572 0.127 -0.287
HMC_vs_Metro 4 0.998 0.327 0.182
HMC_vs_Metro 5 -0.033 0.974 -0.006
HMC_vs_SMC 0 66.973 2.41e-33 12.228
HMC_vs_SMC 1 80.571 1.16e-35 14.710
HMC_vs_SMC 2 82.193 6.54e-36 15.006
HMC_vs_SMC 3 74.650 1.05e-34 13.629
HMC_vs_SMC 4 71.195 4.13e-34 12.998
HMC_vs_SMC 5 66.553 2.89e-33 12.151
Metro_vs_SMC 0 8.295 3.82e-09 1.514
Metro_vs_SMC 1 75.635 7.21e-35 13.809
Metro_vs_SMC 2 72.156 2.81e-34 13.174
Metro_vs_SMC 3 86.406 1.54e-36 15.775
Metro_vs_SMC 4 64.597 6.81e-33 11.794
Metro_vs_SMC 5 66.468 2.99e-33 12.135
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 1.584 0.048 0.013 115.359
HMC 8 2.514 0.065 0.029 83.801
HMC 10 3.222 0.080 0.043 72.939
HMC 12 3.756 0.093 0.059 62.082
HMC 15 4.839 0.092 0.057 83.012
HMC 18 5.719 0.136 0.075 73.946
SMC 5 0.051 0.048 0.013 0.225
SMC 8 0.062 0.065 0.029 -0.111
SMC 10 0.079 0.080 0.043 -0.008
SMC 12 0.079 0.093 0.059 -0.232
SMC 15 0.109 0.092 0.057 0.300
SMC 18 0.116 0.136 0.075 -0.267
Metro 5 0.827 0.048 0.013 58.550
Metro 8 2.569 0.065 0.029 85.674
Metro 10 3.206 0.080 0.043 72.584
Metro 12 3.848 0.093 0.059 63.630
Metro 15 4.732 0.092 0.057 81.155
Metro 18 5.723 0.136 0.075 74.001
DEMetro_Z 5 1.183 0.048 0.013 85.290
DEMetro_Z 8 2.325 0.065 0.029 77.330
DEMetro_Z 10 2.894 0.080 0.043 65.323
DEMetro_Z 12 3.914 0.093 0.059 64.755
DEMetro_Z 15 4.858 0.092 0.057 83.351
DEMetro_Z 18 5.795 0.136 0.075 74.957
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 195.023 1.07e-53 123.600
HMC 8 162.489 5.88e-54 86.344
HMC 10 139.463 5.65e-51 76.356
HMC 12 141.437 1e-52 71.656
HMC 15 145.753 3.68e-51 82.103
HMC 18 165.601 3.81e-57 77.823
SMC 5 1.009 0.318 0.306
SMC 8 -0.601 0.551 -0.139
SMC 10 -0.190 0.85 -0.043
SMC 12 -1.188 0.24 -0.269
SMC 15 1.118 0.268 0.312
SMC 18 -1.763 0.0836 -0.403
Metro 5 8.234 4.4e-09 57.461
Metro 8 198.827 3.01e-63 84.966
Metro 10 157.182 1.99e-55 76.340
Metro 12 151.266 3.98e-55 72.464
Metro 15 149.768 5.15e-52 82.339
Metro 18 188.248 1.48e-63 77.583
DEMetro_Z 5 9.469 2.22e-10 88.887
DEMetro_Z 8 17.049 1.1e-16 78.485
DEMetro_Z 10 17.500 5.37e-17 69.053
DEMetro_Z 12 158.934 1.18e-57 71.515
DEMetro_Z 15 143.957 6.06e-51 81.210
DEMetro_Z 18 150.589 2.36e-53 77.688
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 9.445 2.37e-10 1.724
DEMetro_Z_vs_SMC 1 17.111 1.07e-16 3.124
DEMetro_Z_vs_SMC 2 17.499 5.93e-17 3.195
DEMetro_Z_vs_SMC 3 151.526 1.35e-43 27.665
DEMetro_Z_vs_SMC 4 136.042 3.06e-42 24.838
DEMetro_Z_vs_SMC 5 159.031 3.32e-44 29.035
HMC_vs_Metro 0 9.329 3.12e-10 1.703
HMC_vs_Metro 1 2.433 0.0214 0.444
HMC_vs_Metro 2 0.021 0.983 0.004
HMC_vs_Metro 3 -1.734 0.0936 -0.317
HMC_vs_Metro 4 -0.294 0.771 -0.054
HMC_vs_Metro 5 0.441 0.663 0.080
Metro_vs_DEMetro_Z 0 -2.727 0.0107 -0.498
Metro_vs_DEMetro_Z 1 1.405 0.171 0.256
Metro_vs_DEMetro_Z 2 1.816 0.0797 0.332
Metro_vs_DEMetro_Z 3 1.918 0.0651 0.350
Metro_vs_DEMetro_Z 4 1.696 0.101 0.310
Metro_vs_DEMetro_Z 5 -0.187 0.853 -0.034
HMC_vs_SMC 0 197.548 6.2e-47 36.067
HMC_vs_SMC 1 163.821 1.41e-44 29.909
HMC_vs_SMC 2 142.773 7.56e-43 26.067
HMC_vs_SMC 3 145.005 4.82e-43 26.474
HMC_vs_SMC 4 155.965 5.84e-44 28.475
HMC_vs_SMC 5 158.076 3.96e-44 28.861
Metro_vs_SMC 0 8.132 5.74e-09 1.485
Metro_vs_SMC 1 181.489 7.24e-46 33.135
Metro_vs_SMC 2 165.968 9.65e-45 30.301
Metro_vs_SMC 3 162.638 1.74e-44 29.693
Metro_vs_SMC 4 137.560 2.22e-42 25.115
Metro_vs_SMC 5 210.566 9.76e-48 38.444
HMC_vs_DEMetro_Z 0 3.750 0.000786 0.685
HMC_vs_DEMetro_Z 1 1.696 0.101 0.310
HMC_vs_DEMetro_Z 2 1.885 0.0695 0.344
HMC_vs_DEMetro_Z 3 0.262 0.795 0.048
HMC_vs_DEMetro_Z 4 1.434 0.162 0.262
HMC_vs_DEMetro_Z 5 0.183 0.856 0.033
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.557 0.012 0.004 123.600
HMC 8 0.622 0.012 0.007 86.344
HMC 10 0.622 0.012 0.008 76.356
HMC 12 0.621 0.012 0.008 71.656
HMC 15 0.626 0.010 0.008 82.103
HMC 18 0.627 0.012 0.008 77.823
SMC 5 0.014 0.012 0.004 0.306
SMC 8 0.011 0.012 0.007 -0.139
SMC 10 0.012 0.012 0.008 -0.043
SMC 12 0.010 0.012 0.008 -0.269
SMC 15 0.012 0.010 0.008 0.312
SMC 18 0.009 0.012 0.008 -0.403
Metro 5 0.266 0.012 0.004 57.461
Metro 8 0.613 0.012 0.007 84.966
Metro 10 0.622 0.012 0.008 76.340
Metro 12 0.628 0.012 0.008 72.464
Metro 15 0.628 0.010 0.008 82.339
Metro 18 0.625 0.012 0.008 77.583
DEMetro_Z 5 0.404 0.012 0.004 88.887
DEMetro_Z 8 0.567 0.012 0.007 78.485
DEMetro_Z 10 0.564 0.012 0.008 69.053
DEMetro_Z 12 0.620 0.012 0.008 71.515
DEMetro_Z 15 0.620 0.010 0.008 81.210
DEMetro_Z 18 0.626 0.012 0.008 77.688
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Trace Plots
Pooled
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
8 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
12 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
18 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
8 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
12 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
18 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
5
8
10
12
15
18
Chain
5
8
10
12
15
18

Varying_Mode_Distance_with_heavy_Tails (Mixture, mm, 30 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 3.555 0.000772 1.001
HMC 8 5.003 1.85e-05 3.645
HMC 10 4.679 4.8e-05 3.463
HMC 12 6.005 1.22e-06 6.084
HMC 15 6.383 4.82e-07 9.031
HMC 18 5.733 2.78e-06 6.612
SMC 5 4.620 3.74e-05 1.985
SMC 8 5.068 1.69e-05 4.533
SMC 10 5.550 3.55e-06 3.863
SMC 12 5.170 1.06e-05 3.425
SMC 15 6.345 4.39e-07 5.855
SMC 18 3.912 0.000481 4.950
Metro 5 4.692 3.96e-05 2.698
Metro 8 5.270 7.08e-06 3.122
Metro 10 3.066 0.00384 1.338
Metro 12 3.014 0.00511 3.032
Metro 15 3.980 0.000387 4.054
Metro 18 5.745 1.85e-06 3.718
DEMetro_Z 5 5.776 1.27e-06 3.017
DEMetro_Z 8 6.173 8.26e-07 7.631
DEMetro_Z 10 5.470 5.23e-06 4.758
DEMetro_Z 12 5.240 1.21e-05 8.309
DEMetro_Z 15 6.968 1.08e-07 15.121
DEMetro_Z 18 7.721 1.5e-08 18.256
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -4.271 0.000191 -0.780
HMC_vs_DEMetro_Z 1 -3.285 0.00267 -0.600
HMC_vs_DEMetro_Z 2 -1.184 0.246 -0.216
HMC_vs_DEMetro_Z 3 -1.031 0.311 -0.188
HMC_vs_DEMetro_Z 4 -2.535 0.0169 -0.463
HMC_vs_DEMetro_Z 5 -4.325 0.000164 -0.790
Metro_vs_SMC 0 1.095 0.283 0.200
Metro_vs_SMC 1 -1.388 0.176 -0.253
Metro_vs_SMC 2 -3.243 0.00297 -0.592
Metro_vs_SMC 3 -0.315 0.755 -0.058
Metro_vs_SMC 4 -1.222 0.232 -0.223
Metro_vs_SMC 5 -0.903 0.374 -0.165
Metro_vs_DEMetro_Z 0 -0.375 0.711 -0.068
Metro_vs_DEMetro_Z 1 -3.237 0.00302 -0.591
Metro_vs_DEMetro_Z 2 -3.770 0.000744 -0.688
Metro_vs_DEMetro_Z 3 -2.694 0.0116 -0.492
Metro_vs_DEMetro_Z 4 -4.883 3.51e-05 -0.892
Metro_vs_DEMetro_Z 5 -6.199 9.24e-07 -1.132
HMC_vs_Metro 0 -2.747 0.0102 -0.502
HMC_vs_Metro 1 0.591 0.559 0.108
HMC_vs_Metro 2 2.764 0.00981 0.505
HMC_vs_Metro 3 2.220 0.0344 0.405
HMC_vs_Metro 4 2.697 0.0115 0.492
HMC_vs_Metro 5 2.145 0.0405 0.392
HMC_vs_SMC 0 -2.203 0.0357 -0.402
HMC_vs_SMC 1 -0.742 0.464 -0.135
HMC_vs_SMC 2 -0.427 0.672 -0.078
HMC_vs_SMC 3 2.348 0.0259 0.429
HMC_vs_SMC 4 2.005 0.0544 0.366
HMC_vs_SMC 5 1.596 0.121 0.291
DEMetro_Z_vs_SMC 0 1.606 0.119 0.293
DEMetro_Z_vs_SMC 1 1.975 0.0579 0.361
DEMetro_Z_vs_SMC 2 0.912 0.369 0.167
DEMetro_Z_vs_SMC 3 2.792 0.00918 0.510
DEMetro_Z_vs_SMC 4 4.091 0.000313 0.747
DEMetro_Z_vs_SMC 5 5.248 1.27e-05 0.958
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.094 0.059 0.035 1.001
HMC 8 0.188 0.067 0.033 3.645
HMC 10 0.323 0.102 0.064 3.463
HMC 12 0.540 0.098 0.073 6.084
HMC 15 0.796 0.123 0.074 9.031
HMC 18 0.805 0.115 0.104 6.612
SMC 5 0.129 0.059 0.035 1.985
SMC 8 0.218 0.067 0.033 4.533
SMC 10 0.349 0.102 0.064 3.863
SMC 12 0.347 0.098 0.073 3.425
SMC 15 0.559 0.123 0.074 5.855
SMC 18 0.631 0.115 0.104 4.950
Metro 5 0.154 0.059 0.035 2.698
Metro 8 0.171 0.067 0.033 3.122
Metro 10 0.187 0.102 0.064 1.338
Metro 12 0.318 0.098 0.073 3.032
Metro 15 0.425 0.123 0.074 4.054
Metro 18 0.503 0.115 0.104 3.718
DEMetro_Z 5 0.165 0.059 0.035 3.017
DEMetro_Z 8 0.321 0.067 0.033 7.631
DEMetro_Z 10 0.406 0.102 0.064 4.758
DEMetro_Z 12 0.701 0.098 0.073 8.309
DEMetro_Z 15 1.249 0.123 0.074 15.121
DEMetro_Z 18 2.020 0.115 0.104 18.256
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 -1.411 0.169 -0.259
HMC 8 -0.170 0.866 -0.039
HMC 10 -1.580 0.125 -0.290
HMC 12 0.372 0.711 0.118
HMC 15 0.729 0.471 0.605
HMC 18 -0.982 0.334 -0.179
SMC 5 -1.233 0.227 -0.226
SMC 8 -0.652 0.519 -0.122
SMC 10 -1.713 0.0971 -0.314
SMC 12 -0.587 0.561 -0.115
SMC 15 -1.694 0.1 -0.316
SMC 18 -0.970 0.34 -0.177
Metro 5 -1.237 0.226 -0.227
Metro 8 -1.374 0.179 -0.256
Metro 10 -1.454 0.156 -0.268
Metro 12 0.817 0.42 0.751
Metro 15 -1.320 0.196 -0.249
Metro 18 -0.925 0.363 -0.169
DEMetro_Z 5 -1.182 0.246 -0.218
DEMetro_Z 8 -1.029 0.311 -0.195
DEMetro_Z 10 -1.383 0.177 -0.255
DEMetro_Z 12 -0.188 0.852 -0.037
DEMetro_Z 15 -0.209 0.836 -0.042
DEMetro_Z 18 -0.860 0.397 -0.157
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -1.541 0.134 -0.281
HMC_vs_SMC 1 0.522 0.606 0.095
HMC_vs_SMC 2 1.675 0.105 0.306
HMC_vs_SMC 3 0.959 0.346 0.175
HMC_vs_SMC 4 1.151 0.259 0.210
HMC_vs_SMC 5 -0.605 0.55 -0.111
Metro_vs_DEMetro_Z 0 -0.409 0.686 -0.075
Metro_vs_DEMetro_Z 1 -1.267 0.215 -0.231
Metro_vs_DEMetro_Z 2 -0.647 0.523 -0.118
Metro_vs_DEMetro_Z 3 0.871 0.391 0.159
Metro_vs_DEMetro_Z 4 -2.631 0.0135 -0.480
Metro_vs_DEMetro_Z 5 -1.817 0.0796 -0.332
HMC_vs_Metro 0 -1.799 0.0824 -0.329
HMC_vs_Metro 1 1.440 0.16 0.263
HMC_vs_Metro 2 -1.291 0.207 -0.236
HMC_vs_Metro 3 -0.668 0.509 -0.122
HMC_vs_Metro 4 1.048 0.303 0.191
HMC_vs_Metro 5 -1.024 0.314 -0.187
HMC_vs_DEMetro_Z 0 -2.245 0.0326 -0.410
HMC_vs_DEMetro_Z 1 0.984 0.333 0.180
HMC_vs_DEMetro_Z 2 -2.115 0.0432 -0.386
HMC_vs_DEMetro_Z 3 0.609 0.547 0.111
HMC_vs_DEMetro_Z 4 0.782 0.44 0.143
HMC_vs_DEMetro_Z 5 -3.890 0.000539 -0.710
Metro_vs_SMC 0 -0.038 0.97 -0.007
Metro_vs_SMC 1 -2.336 0.0266 -0.427
Metro_vs_SMC 2 2.802 0.00896 0.512
Metro_vs_SMC 3 0.957 0.347 0.175
Metro_vs_SMC 4 1.170 0.252 0.214
Metro_vs_SMC 5 1.096 0.282 0.200
DEMetro_Z_vs_SMC 0 0.314 0.755 0.057
DEMetro_Z_vs_SMC 1 -1.136 0.265 -0.207
DEMetro_Z_vs_SMC 2 3.818 0.000654 0.697
DEMetro_Z_vs_SMC 3 1.363 0.184 0.249
DEMetro_Z_vs_SMC 4 2.946 0.00628 0.538
DEMetro_Z_vs_SMC 5 4.951 2.9e-05 0.904
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 4.008 12.658 33.375 -0.259
HMC 8 8.338 9.038 17.720 -0.039
HMC 10 4.768 15.206 35.981 -0.290
HMC 12 7.063 5.828 10.481 0.118
HMC 15 14.271 7.481 11.222 0.605
HMC 18 5.745 72.410 371.981 -0.179
SMC 5 5.103 12.658 33.375 -0.226
SMC 8 6.877 9.038 17.720 -0.122
SMC 10 3.909 15.206 35.981 -0.314
SMC 12 4.621 5.828 10.481 -0.115
SMC 15 3.932 7.481 11.222 -0.316
SMC 18 6.549 72.410 371.981 -0.177
Metro 5 5.073 12.658 33.375 -0.227
Metro 8 4.498 9.038 17.720 -0.256
Metro 10 5.575 15.206 35.981 -0.268
Metro 12 13.705 5.828 10.481 0.751
Metro 15 4.689 7.481 11.222 -0.249
Metro 18 9.515 72.410 371.981 -0.169
DEMetro_Z 5 5.392 12.658 33.375 -0.218
DEMetro_Z 8 5.582 9.038 17.720 -0.195
DEMetro_Z 10 6.042 15.206 35.981 -0.255
DEMetro_Z 12 5.436 5.828 10.481 -0.037
DEMetro_Z 15 7.013 7.481 11.222 -0.042
DEMetro_Z 18 13.948 72.410 371.981 -0.157
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 3.550 0.000783 0.993
HMC 8 5.146 1.24e-05 3.858
HMC 10 5.560 3.44e-06 3.862
HMC 12 6.189 7.94e-07 7.755
HMC 15 6.394 4.76e-07 9.725
HMC 18 6.022 1.1e-06 5.519
SMC 5 7.558 4.45e-09 3.743
SMC 8 13.396 3.72e-15 8.530
SMC 10 8.664 4.37e-10 5.788
SMC 12 10.377 4.66e-12 6.770
SMC 15 9.688 4.88e-11 7.957
SMC 18 5.802 2.11e-06 5.538
Metro 5 6.325 1e-07 2.382
Metro 8 6.736 4.39e-08 3.033
Metro 10 4.681 3.23e-05 2.092
Metro 12 4.142 0.00025 4.611
Metro 15 4.894 2.94e-05 5.012
Metro 18 5.449 4.72e-06 3.719
DEMetro_Z 5 9.367 2.49e-12 3.359
DEMetro_Z 8 7.539 1.78e-08 7.994
DEMetro_Z 10 7.232 3.52e-08 6.419
DEMetro_Z 12 6.097 1.12e-06 10.752
DEMetro_Z 15 7.609 1.97e-08 16.195
DEMetro_Z 18 7.854 1.04e-08 15.914
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -2.086 0.0459 -0.381
Metro_vs_DEMetro_Z 1 -4.250 0.000202 -0.776
Metro_vs_DEMetro_Z 2 -4.727 5.41e-05 -0.863
Metro_vs_DEMetro_Z 3 -2.864 0.0077 -0.523
Metro_vs_DEMetro_Z 4 -5.036 2.29e-05 -0.920
Metro_vs_DEMetro_Z 5 -6.479 4.32e-07 -1.183
DEMetro_Z_vs_SMC 0 -0.743 0.463 -0.136
DEMetro_Z_vs_SMC 1 -0.407 0.687 -0.074
DEMetro_Z_vs_SMC 2 0.698 0.491 0.127
DEMetro_Z_vs_SMC 3 2.133 0.0415 0.389
DEMetro_Z_vs_SMC 4 3.714 0.000864 0.678
DEMetro_Z_vs_SMC 5 4.833 4.04e-05 0.882
HMC_vs_DEMetro_Z 0 -7.481 3.03e-08 -1.366
HMC_vs_DEMetro_Z 1 -4.089 0.000314 -0.747
HMC_vs_DEMetro_Z 2 -2.489 0.0188 -0.454
HMC_vs_DEMetro_Z 3 -1.207 0.237 -0.220
HMC_vs_DEMetro_Z 4 -2.672 0.0123 -0.488
HMC_vs_DEMetro_Z 5 -4.609 7.51e-05 -0.841
HMC_vs_Metro 0 -3.534 0.00139 -0.645
HMC_vs_Metro 1 0.928 0.361 0.169
HMC_vs_Metro 2 2.353 0.0256 0.430
HMC_vs_Metro 3 1.924 0.0642 0.351
HMC_vs_Metro 4 2.402 0.0229 0.439
HMC_vs_Metro 5 1.559 0.13 0.285
HMC_vs_SMC 0 -5.976 1.7e-06 -1.091
HMC_vs_SMC 1 -4.347 0.000155 -0.794
HMC_vs_SMC 2 -2.194 0.0364 -0.401
HMC_vs_SMC 3 0.684 0.5 0.125
HMC_vs_SMC 4 1.161 0.255 0.212
HMC_vs_SMC 5 -0.024 0.981 -0.004
Metro_vs_SMC 0 -2.641 0.0132 -0.482
Metro_vs_SMC 1 -6.880 1.47e-07 -1.256
Metro_vs_SMC 2 -4.695 5.92e-05 -0.857
Metro_vs_SMC 3 -1.632 0.113 -0.298
Metro_vs_SMC 4 -2.089 0.0456 -0.381
Metro_vs_SMC 5 -1.647 0.11 -0.301
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.180 0.131 0.049 0.993
HMC 8 0.293 0.144 0.039 3.858
HMC 10 0.381 0.176 0.053 3.862
HMC 12 0.587 0.162 0.055 7.755
HMC 15 0.817 0.184 0.065 9.725
HMC 18 0.808 0.192 0.112 5.519
SMC 5 0.315 0.131 0.049 3.743
SMC 8 0.474 0.144 0.039 8.530
SMC 10 0.483 0.176 0.053 5.788
SMC 12 0.533 0.162 0.055 6.770
SMC 15 0.702 0.184 0.065 7.957
SMC 18 0.811 0.192 0.112 5.538
Metro 5 0.248 0.131 0.049 2.382
Metro 8 0.261 0.144 0.039 3.033
Metro 10 0.287 0.176 0.053 2.092
Metro 12 0.415 0.162 0.055 4.611
Metro 15 0.510 0.184 0.065 5.012
Metro 18 0.607 0.192 0.112 3.719
DEMetro_Z 5 0.296 0.131 0.049 3.359
DEMetro_Z 8 0.453 0.144 0.039 7.994
DEMetro_Z 10 0.516 0.176 0.053 6.419
DEMetro_Z 12 0.751 0.162 0.055 10.752
DEMetro_Z 15 1.238 0.184 0.065 16.195
DEMetro_Z 18 1.970 0.192 0.112 15.914
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 5.068 1.03e-05 2.413
HMC 8 5.447 6.09e-06 5.738
HMC 10 5.470 5.42e-06 5.123
HMC 12 6.131 9.47e-07 8.031
HMC 15 6.164 9.29e-07 10.845
HMC 18 5.391 8.37e-06 16.173
SMC 5 9.518 6.82e-11 7.483
SMC 8 9.053 3.43e-10 9.435
SMC 10 6.931 8.56e-08 6.531
SMC 12 6.590 1.95e-07 5.296
SMC 15 6.910 9.85e-08 7.293
SMC 18 4.052 0.000344 13.094
Metro 5 6.201 4.05e-07 3.589
Metro 8 6.082 6.95e-07 4.026
Metro 10 3.944 0.000348 2.101
Metro 12 5.915 9.26e-07 3.321
Metro 15 4.464 0.000102 4.996
Metro 18 6.189 8.25e-07 8.712
DEMetro_Z 5 9.703 2.98e-11 6.624
DEMetro_Z 8 6.635 2.54e-07 11.388
DEMetro_Z 10 6.015 1.27e-06 7.206
DEMetro_Z 12 5.190 1.44e-05 11.257
DEMetro_Z 15 6.778 1.85e-07 18.730
DEMetro_Z 18 7.501 2.85e-08 48.873
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 -0.873 0.39 -0.159
DEMetro_Z_vs_SMC 1 0.906 0.372 0.166
DEMetro_Z_vs_SMC 2 0.513 0.612 0.094
DEMetro_Z_vs_SMC 3 2.483 0.0191 0.453
DEMetro_Z_vs_SMC 4 4.005 0.000395 0.731
DEMetro_Z_vs_SMC 5 5.184 1.52e-05 0.946
HMC_vs_Metro 0 -1.982 0.057 -0.362
HMC_vs_Metro 1 1.241 0.224 0.227
HMC_vs_Metro 2 3.074 0.00457 0.561
HMC_vs_Metro 3 3.107 0.00421 0.567
HMC_vs_Metro 4 2.646 0.013 0.483
HMC_vs_Metro 5 2.216 0.0347 0.405
Metro_vs_DEMetro_Z 0 -3.560 0.0013 -0.650
Metro_vs_DEMetro_Z 1 -3.810 0.000668 -0.696
Metro_vs_DEMetro_Z 2 -4.235 0.00021 -0.773
Metro_vs_DEMetro_Z 3 -3.497 0.00153 -0.639
Metro_vs_DEMetro_Z 4 -4.871 3.63e-05 -0.889
Metro_vs_DEMetro_Z 5 -6.296 7.1e-07 -1.149
HMC_vs_SMC 0 -5.609 4.68e-06 -1.024
HMC_vs_SMC 1 -2.362 0.0251 -0.431
HMC_vs_SMC 2 -1.201 0.24 -0.219
HMC_vs_SMC 3 1.860 0.073 0.340
HMC_vs_SMC 4 1.849 0.0746 0.338
HMC_vs_SMC 5 1.283 0.21 0.234
Metro_vs_SMC 0 -4.440 0.00012 -0.811
Metro_vs_SMC 1 -4.570 8.37e-05 -0.834
Metro_vs_SMC 2 -4.303 0.000175 -0.786
Metro_vs_SMC 3 -2.024 0.0523 -0.370
Metro_vs_SMC 4 -1.388 0.176 -0.253
Metro_vs_SMC 5 -1.271 0.214 -0.232
HMC_vs_DEMetro_Z 0 -6.436 4.85e-07 -1.175
HMC_vs_DEMetro_Z 1 -3.069 0.00462 -0.560
HMC_vs_DEMetro_Z 2 -1.478 0.15 -0.270
HMC_vs_DEMetro_Z 3 -1.114 0.274 -0.203
HMC_vs_DEMetro_Z 4 -2.514 0.0177 -0.459
HMC_vs_DEMetro_Z 5 -4.458 0.000114 -0.814
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.022 0.012 0.004 2.413
HMC 8 0.034 0.011 0.004 5.738
HMC 10 0.048 0.013 0.007 5.123
HMC 12 0.069 0.012 0.007 8.031
HMC 15 0.085 0.012 0.007 10.845
HMC 18 0.072 0.009 0.004 16.173
SMC 5 0.044 0.012 0.004 7.483
SMC 8 0.049 0.011 0.004 9.435
SMC 10 0.058 0.013 0.007 6.531
SMC 12 0.049 0.012 0.007 5.296
SMC 15 0.061 0.012 0.007 7.293
SMC 18 0.060 0.009 0.004 13.094
Metro 5 0.027 0.012 0.004 3.589
Metro 8 0.027 0.011 0.004 4.026
Metro 10 0.028 0.013 0.007 2.101
Metro 12 0.035 0.012 0.007 3.321
Metro 15 0.045 0.012 0.007 4.996
Metro 18 0.043 0.009 0.004 8.712
DEMetro_Z 5 0.040 0.012 0.004 6.624
DEMetro_Z 8 0.057 0.011 0.004 11.388
DEMetro_Z 10 0.063 0.013 0.007 7.206
DEMetro_Z 12 0.091 0.012 0.007 11.257
DEMetro_Z 15 0.138 0.012 0.007 18.730
DEMetro_Z 18 0.201 0.009 0.004 48.873
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 3.108 0.00332 1.241
HMC 8 4.156 0.000228 3.538
HMC 10 5.077 1.56e-05 4.023
HMC 12 6.226 5.79e-07 5.275
HMC 15 4.774 4.28e-05 5.662
HMC 18 7.194 4.03e-08 6.583
SMC 5 3.135 0.0031 1.268
SMC 8 4.309 0.000149 3.811
SMC 10 5.114 1.07e-05 2.858
SMC 12 5.247 8.66e-06 3.619
SMC 15 6.221 6e-07 5.425
SMC 18 4.912 2.84e-05 5.445
Metro 5 4.929 2.28e-05 3.541
Metro 8 3.620 0.00098 2.664
Metro 10 4.140 0.000195 2.190
Metro 12 3.026 0.00497 3.217
Metro 15 4.639 6.29e-05 5.583
Metro 18 4.087 0.000303 6.339
DEMetro_Z 5 6.151 4.2e-07 3.320
DEMetro_Z 8 6.850 1.11e-07 6.750
DEMetro_Z 10 4.364 9.02e-05 2.035
DEMetro_Z 12 4.220 0.000208 5.931
DEMetro_Z 15 5.147 1.64e-05 13.088
DEMetro_Z 18 5.251 1.24e-05 17.678
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -3.843 0.000611 -0.702
HMC_vs_DEMetro_Z 1 -2.605 0.0143 -0.476
HMC_vs_DEMetro_Z 2 2.217 0.0346 0.405
HMC_vs_DEMetro_Z 3 -0.381 0.706 -0.070
HMC_vs_DEMetro_Z 4 -2.470 0.0196 -0.451
HMC_vs_DEMetro_Z 5 -2.864 0.00769 -0.523
Metro_vs_SMC 0 3.015 0.00529 0.551
Metro_vs_SMC 1 -0.923 0.364 -0.169
Metro_vs_SMC 2 -1.203 0.239 -0.220
Metro_vs_SMC 3 -0.297 0.769 -0.054
Metro_vs_SMC 4 0.102 0.92 0.019
Metro_vs_SMC 5 0.477 0.637 0.087
Metro_vs_DEMetro_Z 0 0.268 0.791 0.049
Metro_vs_DEMetro_Z 1 -3.233 0.00305 -0.590
Metro_vs_DEMetro_Z 2 0.223 0.825 0.041
Metro_vs_DEMetro_Z 3 -1.650 0.11 -0.301
Metro_vs_DEMetro_Z 4 -2.491 0.0187 -0.455
Metro_vs_DEMetro_Z 5 -3.619 0.00111 -0.661
HMC_vs_Metro 0 -2.755 0.01 -0.503
HMC_vs_Metro 1 0.750 0.459 0.137
HMC_vs_Metro 2 1.888 0.0691 0.345
HMC_vs_Metro 3 1.476 0.151 0.269
HMC_vs_Metro 4 0.041 0.967 0.008
HMC_vs_Metro 5 0.119 0.906 0.022
HMC_vs_SMC 0 -0.053 0.958 -0.010
HMC_vs_SMC 1 -0.204 0.84 -0.037
HMC_vs_SMC 2 1.106 0.278 0.202
HMC_vs_SMC 3 1.687 0.102 0.308
HMC_vs_SMC 4 0.153 0.88 0.028
HMC_vs_SMC 5 0.783 0.44 0.143
DEMetro_Z_vs_SMC 0 3.185 0.00345 0.582
DEMetro_Z_vs_SMC 1 2.265 0.0312 0.414
DEMetro_Z_vs_SMC 2 -1.260 0.218 -0.230
DEMetro_Z_vs_SMC 3 1.416 0.167 0.259
DEMetro_Z_vs_SMC 4 2.956 0.00614 0.540
DEMetro_Z_vs_SMC 5 3.499 0.00153 0.639
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.103 0.059 0.035 1.241
HMC 8 0.185 0.067 0.033 3.538
HMC 10 0.359 0.102 0.064 4.023
HMC 12 0.481 0.098 0.073 5.275
HMC 15 0.545 0.123 0.074 5.662
HMC 18 0.802 0.115 0.104 6.583
SMC 5 0.103 0.059 0.035 1.268
SMC 8 0.194 0.067 0.033 3.811
SMC 10 0.284 0.102 0.064 2.858
SMC 12 0.361 0.098 0.073 3.619
SMC 15 0.527 0.123 0.074 5.425
SMC 18 0.683 0.115 0.104 5.445
Metro 5 0.184 0.059 0.035 3.541
Metro 8 0.156 0.067 0.033 2.664
Metro 10 0.242 0.102 0.064 2.190
Metro 12 0.332 0.098 0.073 3.217
Metro 15 0.539 0.123 0.074 5.583
Metro 18 0.776 0.115 0.104 6.339
DEMetro_Z 5 0.176 0.059 0.035 3.320
DEMetro_Z 8 0.292 0.067 0.033 6.750
DEMetro_Z 10 0.232 0.102 0.064 2.035
DEMetro_Z 12 0.528 0.098 0.073 5.931
DEMetro_Z 15 1.098 0.123 0.074 13.088
DEMetro_Z 18 1.959 0.115 0.104 17.678
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 -1.368 0.182 -0.251
HMC 8 -1.469 0.152 -0.274
HMC 10 -0.831 0.41 -0.174
HMC 12 -0.430 0.669 -0.096
HMC 15 -1.224 0.228 -0.245
HMC 18 -0.849 0.402 -0.156
SMC 5 -1.506 0.143 -0.276
SMC 8 -1.238 0.225 -0.230
SMC 10 -1.795 0.083 -0.329
SMC 12 -1.295 0.203 -0.252
SMC 15 -1.953 0.0597 -0.365
SMC 18 -0.970 0.34 -0.177
Metro 5 -0.993 0.328 -0.190
Metro 8 -1.044 0.303 -0.208
Metro 10 -1.565 0.128 -0.287
Metro 12 0.378 0.707 0.099
Metro 15 0.754 0.456 0.576
Metro 18 -0.952 0.349 -0.174
DEMetro_Z 5 -1.300 0.204 -0.239
DEMetro_Z 8 -1.489 0.147 -0.276
DEMetro_Z 10 -1.506 0.143 -0.277
DEMetro_Z 12 0.009 0.993 0.002
DEMetro_Z 15 -0.264 0.793 -0.056
DEMetro_Z 18 -0.813 0.423 -0.149
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 1.824 0.0784 0.333
HMC_vs_SMC 1 -1.025 0.314 -0.187
HMC_vs_SMC 2 1.476 0.151 0.270
HMC_vs_SMC 3 1.357 0.185 0.248
HMC_vs_SMC 4 1.586 0.124 0.290
HMC_vs_SMC 5 1.231 0.228 0.225
Metro_vs_DEMetro_Z 0 0.923 0.364 0.168
Metro_vs_DEMetro_Z 1 0.819 0.419 0.150
Metro_vs_DEMetro_Z 2 -1.089 0.285 -0.199
Metro_vs_DEMetro_Z 3 0.523 0.605 0.096
Metro_vs_DEMetro_Z 4 0.834 0.411 0.152
Metro_vs_DEMetro_Z 5 -3.245 0.00295 -0.593
HMC_vs_Metro 0 -1.114 0.274 -0.203
HMC_vs_Metro 1 -0.763 0.452 -0.139
HMC_vs_Metro 2 1.077 0.29 0.197
HMC_vs_Metro 3 -0.914 0.368 -0.167
HMC_vs_Metro 4 -1.097 0.282 -0.200
HMC_vs_Metro 5 1.022 0.315 0.187
HMC_vs_DEMetro_Z 0 -1.442 0.16 -0.263
HMC_vs_DEMetro_Z 1 0.075 0.94 0.014
HMC_vs_DEMetro_Z 2 0.957 0.346 0.175
HMC_vs_DEMetro_Z 3 -0.782 0.441 -0.143
HMC_vs_DEMetro_Z 4 -1.525 0.138 -0.278
HMC_vs_DEMetro_Z 5 -0.458 0.65 -0.084
Metro_vs_SMC 0 1.580 0.125 0.288
Metro_vs_SMC 1 0.246 0.807 0.045
Metro_vs_SMC 2 4.116 0.000292 0.751
Metro_vs_SMC 3 2.047 0.0498 0.374
Metro_vs_SMC 4 1.263 0.216 0.231
Metro_vs_SMC 5 1.046 0.304 0.191
DEMetro_Z_vs_SMC 0 2.729 0.0107 0.498
DEMetro_Z_vs_SMC 1 -1.153 0.258 -0.210
DEMetro_Z_vs_SMC 2 5.016 2.43e-05 0.916
DEMetro_Z_vs_SMC 3 4.126 0.000284 0.753
DEMetro_Z_vs_SMC 4 3.184 0.00345 0.581
DEMetro_Z_vs_SMC 5 3.138 0.00388 0.573
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 4.265 12.658 33.375 -0.251
HMC 8 4.190 9.038 17.720 -0.274
HMC 10 8.932 15.206 35.981 -0.174
HMC 12 4.821 5.828 10.481 -0.096
HMC 15 4.735 7.481 11.222 -0.245
HMC 18 14.463 72.410 371.981 -0.156
SMC 5 3.435 12.658 33.375 -0.276
SMC 8 4.964 9.038 17.720 -0.230
SMC 10 3.367 15.206 35.981 -0.329
SMC 12 3.183 5.828 10.481 -0.252
SMC 15 3.388 7.481 11.222 -0.365
SMC 18 6.524 72.410 371.981 -0.177
Metro 5 6.331 12.658 33.375 -0.190
Metro 8 5.353 9.038 17.720 -0.208
Metro 10 4.870 15.206 35.981 -0.287
Metro 12 6.871 5.828 10.481 0.099
Metro 15 13.943 7.481 11.222 0.576
Metro 18 7.723 72.410 371.981 -0.174
DEMetro_Z 5 4.688 12.658 33.375 -0.239
DEMetro_Z 8 4.144 9.038 17.720 -0.276
DEMetro_Z 10 5.241 15.206 35.981 -0.277
DEMetro_Z 12 5.848 5.828 10.481 0.002
DEMetro_Z 15 6.857 7.481 11.222 -0.056
DEMetro_Z 18 17.136 72.410 371.981 -0.149
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 4.024 0.000187 1.283
HMC 8 4.730 3.76e-05 2.974
HMC 10 5.720 2.58e-06 5.130
HMC 12 6.433 3.76e-07 6.908
HMC 15 4.795 4.1e-05 6.186
HMC 18 7.224 3.19e-08 5.745
SMC 5 4.286 0.000102 1.762
SMC 8 8.278 1.24e-09 5.485
SMC 10 6.854 5.72e-08 4.001
SMC 12 6.251 5.26e-07 5.129
SMC 15 8.234 1.98e-09 6.535
SMC 18 5.970 1.21e-06 5.045
Metro 5 5.912 6.98e-07 2.799
Metro 8 5.131 1.16e-05 3.286
Metro 10 5.095 1.12e-05 2.808
Metro 12 3.731 0.000779 4.245
Metro 15 4.822 3.81e-05 6.311
Metro 18 4.163 0.000242 5.479
DEMetro_Z 5 9.534 7.77e-13 3.176
DEMetro_Z 8 7.741 7.26e-09 5.972
DEMetro_Z 10 7.862 1.45e-09 3.698
DEMetro_Z 12 4.948 2.77e-05 8.286
DEMetro_Z 15 5.346 9.45e-06 14.894
DEMetro_Z 18 5.584 4.87e-06 15.230
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -0.759 0.454 -0.139
Metro_vs_DEMetro_Z 1 -2.531 0.017 -0.462
Metro_vs_DEMetro_Z 2 -1.367 0.182 -0.249
Metro_vs_DEMetro_Z 3 -2.098 0.0448 -0.383
Metro_vs_DEMetro_Z 4 -2.689 0.0118 -0.491
Metro_vs_DEMetro_Z 5 -3.814 0.00066 -0.696
DEMetro_Z_vs_SMC 0 3.138 0.00389 0.573
DEMetro_Z_vs_SMC 1 0.535 0.597 0.098
DEMetro_Z_vs_SMC 2 -0.419 0.678 -0.077
DEMetro_Z_vs_SMC 3 1.570 0.127 0.287
DEMetro_Z_vs_SMC 4 2.991 0.00562 0.546
DEMetro_Z_vs_SMC 5 3.653 0.00102 0.667
HMC_vs_DEMetro_Z 0 -6.027 1.48e-06 -1.100
HMC_vs_DEMetro_Z 1 -3.343 0.0023 -0.610
HMC_vs_DEMetro_Z 2 1.363 0.183 0.249
HMC_vs_DEMetro_Z 3 -0.673 0.506 -0.123
HMC_vs_DEMetro_Z 4 -2.616 0.014 -0.478
HMC_vs_DEMetro_Z 5 -3.026 0.00515 -0.552
HMC_vs_Metro 0 -2.817 0.00863 -0.514
HMC_vs_Metro 1 -0.331 0.743 -0.060
HMC_vs_Metro 2 2.132 0.0416 0.389
HMC_vs_Metro 3 1.651 0.11 0.301
HMC_vs_Metro 4 -0.062 0.951 -0.011
HMC_vs_Metro 5 0.153 0.879 0.028
HMC_vs_SMC 0 -1.097 0.282 -0.200
HMC_vs_SMC 1 -2.577 0.0153 -0.470
HMC_vs_SMC 2 1.023 0.315 0.187
HMC_vs_SMC 3 1.488 0.148 0.272
HMC_vs_SMC 4 -0.228 0.821 -0.042
HMC_vs_SMC 5 0.613 0.545 0.112
Metro_vs_SMC 0 1.719 0.0962 0.314
Metro_vs_SMC 1 -2.210 0.0352 -0.403
Metro_vs_SMC 2 -2.274 0.0305 -0.415
Metro_vs_SMC 3 -0.596 0.556 -0.109
Metro_vs_SMC 4 -0.140 0.89 -0.026
Metro_vs_SMC 5 0.288 0.775 0.053
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.194 0.131 0.049 1.283
HMC 8 0.259 0.144 0.039 2.974
HMC 10 0.448 0.176 0.053 5.130
HMC 12 0.541 0.162 0.055 6.908
HMC 15 0.586 0.184 0.065 6.186
HMC 18 0.834 0.192 0.112 5.745
SMC 5 0.217 0.131 0.049 1.762
SMC 8 0.356 0.144 0.039 5.485
SMC 10 0.388 0.176 0.053 4.001
SMC 12 0.443 0.162 0.055 5.129
SMC 15 0.609 0.184 0.065 6.535
SMC 18 0.755 0.192 0.112 5.045
Metro 5 0.268 0.131 0.049 2.799
Metro 8 0.271 0.144 0.039 3.286
Metro 10 0.325 0.176 0.053 2.808
Metro 12 0.395 0.162 0.055 4.245
Metro 15 0.595 0.184 0.065 6.311
Metro 18 0.804 0.192 0.112 5.479
DEMetro_Z 5 0.287 0.131 0.049 3.176
DEMetro_Z 8 0.375 0.144 0.039 5.972
DEMetro_Z 10 0.372 0.176 0.053 3.698
DEMetro_Z 12 0.616 0.162 0.055 8.286
DEMetro_Z 15 1.153 0.184 0.065 14.894
DEMetro_Z 18 1.893 0.192 0.112 15.230
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 5 5.123 1.18e-05 3.291
HMC 8 4.403 0.000122 5.096
HMC 10 5.408 6.81e-06 5.725
HMC 12 6.853 1.16e-07 7.283
HMC 15 4.684 5.72e-05 6.873
HMC 18 6.823 1.6e-07 15.272
SMC 5 4.981 2.09e-05 4.077
SMC 8 6.152 8.62e-07 7.281
SMC 10 5.959 1.17e-06 4.642
SMC 12 5.562 4.07e-06 4.977
SMC 15 6.640 2.02e-07 6.696
SMC 18 5.009 2.42e-05 14.170
Metro 5 6.292 3.74e-07 4.187
Metro 8 6.766 9.02e-08 4.417
Metro 10 4.677 4.22e-05 2.754
Metro 12 2.533 0.0168 3.776
Metro 15 5.972 1.15e-06 4.782
Metro 18 3.826 0.000637 16.098
DEMetro_Z 5 13.505 3.54e-17 5.349
DEMetro_Z 8 7.171 4.91e-08 7.796
DEMetro_Z 10 6.556 1.22e-07 3.560
DEMetro_Z 12 4.179 0.000238 8.044
DEMetro_Z 15 4.931 3.03e-05 16.453
DEMetro_Z 18 5.149 1.67e-05 46.598
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 1.450 0.158 0.265
DEMetro_Z_vs_SMC 1 0.316 0.754 0.058
DEMetro_Z_vs_SMC 2 -1.145 0.261 -0.209
DEMetro_Z_vs_SMC 3 1.345 0.189 0.246
DEMetro_Z_vs_SMC 4 2.861 0.00776 0.522
DEMetro_Z_vs_SMC 5 3.427 0.00184 0.626
HMC_vs_Metro 0 -0.900 0.375 -0.164
HMC_vs_Metro 1 0.505 0.618 0.092
HMC_vs_Metro 2 2.273 0.0306 0.415
HMC_vs_Metro 3 1.864 0.0724 0.340
HMC_vs_Metro 4 1.139 0.264 0.208
HMC_vs_Metro 5 -0.153 0.88 -0.028
Metro_vs_DEMetro_Z 0 -1.545 0.133 -0.282
Metro_vs_DEMetro_Z 1 -2.635 0.0134 -0.481
Metro_vs_DEMetro_Z 2 -1.119 0.272 -0.204
Metro_vs_DEMetro_Z 3 -1.765 0.0881 -0.322
Metro_vs_DEMetro_Z 4 -3.418 0.00189 -0.624
Metro_vs_DEMetro_Z 5 -3.613 0.00113 -0.660
HMC_vs_SMC 0 -0.777 0.444 -0.142
HMC_vs_SMC 1 -1.203 0.239 -0.220
HMC_vs_SMC 2 0.777 0.443 0.142
HMC_vs_SMC 3 1.855 0.0738 0.339
HMC_vs_SMC 4 0.097 0.923 0.018
HMC_vs_SMC 5 0.297 0.769 0.054
Metro_vs_SMC 0 0.099 0.922 0.018
Metro_vs_SMC 1 -1.986 0.0566 -0.363
Metro_vs_SMC 2 -2.420 0.022 -0.442
Metro_vs_SMC 3 -0.649 0.522 -0.118
Metro_vs_SMC 4 -1.466 0.153 -0.268
Metro_vs_SMC 5 0.383 0.705 0.070
HMC_vs_DEMetro_Z 0 -2.812 0.00875 -0.513
HMC_vs_DEMetro_Z 1 -1.804 0.0816 -0.329
HMC_vs_DEMetro_Z 2 1.834 0.077 0.335
HMC_vs_DEMetro_Z 3 -0.330 0.743 -0.060
HMC_vs_DEMetro_Z 4 -2.429 0.0216 -0.443
HMC_vs_DEMetro_Z 5 -3.029 0.00512 -0.553
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 5 0.026 0.012 0.004 3.291
HMC 8 0.031 0.011 0.004 5.096
HMC 10 0.053 0.013 0.007 5.725
HMC 12 0.063 0.012 0.007 7.283
HMC 15 0.058 0.012 0.007 6.873
HMC 18 0.069 0.009 0.004 15.272
SMC 5 0.030 0.012 0.004 4.077
SMC 8 0.040 0.011 0.004 7.281
SMC 10 0.045 0.013 0.007 4.642
SMC 12 0.047 0.012 0.007 4.977
SMC 15 0.057 0.012 0.007 6.696
SMC 18 0.065 0.009 0.004 14.170
Metro 5 0.030 0.012 0.004 4.187
Metro 8 0.029 0.011 0.004 4.417
Metro 10 0.032 0.013 0.007 2.754
Metro 12 0.038 0.012 0.007 3.776
Metro 15 0.044 0.012 0.007 4.782
Metro 18 0.072 0.009 0.004 16.098
DEMetro_Z 5 0.035 0.012 0.004 5.349
DEMetro_Z 8 0.042 0.011 0.004 7.796
DEMetro_Z 10 0.038 0.013 0.007 3.560
DEMetro_Z 12 0.069 0.012 0.007 8.044
DEMetro_Z 15 0.123 0.012 0.007 16.453
DEMetro_Z 18 0.192 0.009 0.004 46.598
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Trace Plots
Pooled
5 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
8 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
12 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
15 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
18 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
5 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
8 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
12 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
15 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
18 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
5
8
10
12
15
18
Chain
5
8
10
12
15
18

two_attr_tails

▼

Varying_Tails_with_high_Dimension (MvStudentT, nu, 30 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 2.036 0.0507 3.524
HMC 3.0 1.395 0.173 2.640
HMC 4.0 0.175 0.863 0.128
HMC 10.0 -2.814 0.00674 -0.667
HMC 50.0 -4.256 8.01e-05 -1.008
SMC 2.1 52.414 3.61e-31 68.951
SMC 3.0 39.400 3.72e-27 69.167
SMC 4.0 29.632 2.06e-23 72.257
SMC 10.0 39.163 2.17e-27 52.185
SMC 50.0 23.260 3.35e-21 23.047
Metro 2.1 2.616 0.014 22.000
Metro 3.0 11.205 9.1e-13 8.143
Metro 4.0 13.972 1.47e-15 9.364
Metro 10.0 18.394 2.28e-21 8.009
Metro 50.0 15.200 2.64e-18 6.735
DEMetro_Z 2.1 23.648 1.66e-20 366.943
DEMetro_Z 3.0 21.050 4.07e-19 413.531
DEMetro_Z 4.0 25.177 2.93e-21 436.403
DEMetro_Z 10.0 24.472 6.38e-21 273.772
DEMetro_Z 50.0 13.268 7.59e-14 286.124
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -22.716 5.07e-20 -4.147
HMC_vs_DEMetro_Z 1 -21.072 3.97e-19 -3.847
HMC_vs_DEMetro_Z 2 -25.418 2.26e-21 -4.641
HMC_vs_DEMetro_Z 3 -24.437 6.75e-21 -4.462
HMC_vs_DEMetro_Z 4 -13.307 7.06e-14 -2.430
Metro_vs_SMC 0 -5.473 6.81e-06 -0.999
Metro_vs_SMC 1 -29.536 3.41e-23 -5.392
Metro_vs_SMC 2 -24.709 4.97e-21 -4.511
Metro_vs_SMC 3 -33.992 6.47e-25 -6.206
Metro_vs_SMC 4 -17.285 8.21e-17 -3.156
Metro_vs_DEMetro_Z 0 -19.651 2.64e-18 -3.588
Metro_vs_DEMetro_Z 1 -20.438 9.12e-19 -3.731
Metro_vs_DEMetro_Z 2 -24.965 3.73e-21 -4.558
Metro_vs_DEMetro_Z 3 -23.709 1.56e-20 -4.329
Metro_vs_DEMetro_Z 4 -12.949 1.4e-13 -2.364
HMC_vs_Metro 0 -2.163 0.0389 -0.395
HMC_vs_Metro 1 -2.915 0.00679 -0.532
HMC_vs_Metro 2 -9.697 1.32e-10 -1.770
HMC_vs_Metro 3 -19.805 2.14e-18 -3.616
HMC_vs_Metro 4 -18.671 1.05e-17 -3.409
HMC_vs_SMC 0 -28.730 7.4e-23 -5.245
HMC_vs_SMC 1 -23.165 2.96e-20 -4.229
HMC_vs_SMC 2 -29.102 5.16e-23 -5.313
HMC_vs_SMC 3 -39.437 9.51e-27 -7.200
HMC_vs_SMC 4 -24.927 3.89e-21 -4.551
DEMetro_Z_vs_SMC 0 19.300 4.3e-18 3.524
DEMetro_Z_vs_SMC 1 18.254 1.92e-17 3.333
DEMetro_Z_vs_SMC 2 20.730 6.2e-19 3.785
DEMetro_Z_vs_SMC 3 20.244 1.18e-18 3.696
DEMetro_Z_vs_SMC 4 12.227 5.74e-13 2.232
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.148 0.070 0.022 3.524
HMC 3.0 0.053 0.038 0.005 2.640
HMC 4.0 0.033 0.032 0.004 0.128
HMC 10.0 0.022 0.024 0.003 -0.667
HMC 50.0 0.020 0.022 0.003 -1.008
SMC 2.1 1.602 0.070 0.022 68.951
SMC 3.0 0.415 0.038 0.005 69.167
SMC 4.0 0.309 0.032 0.004 72.257
SMC 10.0 0.195 0.024 0.003 52.185
SMC 50.0 0.088 0.022 0.003 23.047
Metro 2.1 0.559 0.070 0.022 22.000
Metro 3.0 0.083 0.038 0.005 8.143
Metro 4.0 0.068 0.032 0.004 9.364
Metro 10.0 0.050 0.024 0.003 8.009
Metro 50.0 0.042 0.022 0.003 6.735
DEMetro_Z 2.1 8.224 0.070 0.022 366.943
DEMetro_Z 3.0 2.292 0.038 0.005 413.531
DEMetro_Z 4.0 1.705 0.032 0.004 436.403
DEMetro_Z 10.0 0.922 0.024 0.003 273.772
DEMetro_Z 50.0 0.836 0.022 0.003 286.124
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -0.911 0.368 -0.176
HMC 3.0 1.073 0.29 0.592
HMC 4.0 2.812 0.0067 0.722
HMC 10.0 5.779 1.09e-06 2.776
HMC 50.0 10.082 2.59e-13 3.643
SMC 2.1 217.095 1.25e-52 171.585
SMC 3.0 220.335 9.99e-50 306.734
SMC 4.0 160.497 2.38e-44 1475.303
SMC 10.0 120.910 9.29e-41 12818.266
SMC 50.0 53.938 1.22e-30 1713.122
Metro 2.1 1.113 0.275 34.033
Metro 3.0 1.965 0.0545 0.453
Metro 4.0 5.049 7.87e-06 1.923
Metro 10.0 13.387 9.46e-15 10.380
Metro 50.0 17.249 1.52e-19 8.530
DEMetro_Z 2.1 15.288 1.86e-15 55.358
DEMetro_Z 3.0 12.112 7.02e-13 68.168
DEMetro_Z 4.0 12.787 1.9e-13 308.941
DEMetro_Z 10.0 15.533 1.36e-15 1628.366
DEMetro_Z 50.0 7.605 2.2e-08 1758.242
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -219.139 3.07e-48 -40.009
HMC_vs_SMC 1 -206.060 1.83e-47 -37.621
HMC_vs_SMC 2 -160.629 2.49e-44 -29.327
HMC_vs_SMC 3 -120.885 9.35e-41 -22.071
HMC_vs_SMC 4 -53.838 1.29e-30 -9.829
Metro_vs_DEMetro_Z 0 -0.707 0.485 -0.129
Metro_vs_DEMetro_Z 1 -12.024 8.64e-13 -2.195
Metro_vs_DEMetro_Z 2 -12.738 2.1e-13 -2.326
Metro_vs_DEMetro_Z 3 -15.420 1.64e-15 -2.815
Metro_vs_DEMetro_Z 4 -7.575 2.37e-08 -1.383
HMC_vs_Metro 0 -1.119 0.272 -0.204
HMC_vs_Metro 1 0.267 0.791 0.049
HMC_vs_Metro 2 -3.618 0.00112 -0.661
HMC_vs_Metro 3 -8.249 4.28e-09 -1.506
HMC_vs_Metro 4 -9.622 1.57e-10 -1.757
HMC_vs_DEMetro_Z 0 -15.376 1.77e-15 -2.807
HMC_vs_DEMetro_Z 1 -11.941 1.02e-12 -2.180
HMC_vs_DEMetro_Z 2 -12.769 1.97e-13 -2.331
HMC_vs_DEMetro_Z 3 -15.477 1.49e-15 -2.826
HMC_vs_DEMetro_Z 4 -7.591 2.28e-08 -1.386
Metro_vs_SMC 0 -4.488 0.000105 -0.819
Metro_vs_SMC 1 -233.163 5.09e-49 -42.570
Metro_vs_SMC 2 -161.346 2.19e-44 -29.458
Metro_vs_SMC 3 -120.500 1.03e-40 -22.000
Metro_vs_SMC 4 -53.629 1.44e-30 -9.791
DEMetro_Z_vs_SMC 0 -33.538 9.47e-25 -6.123
DEMetro_Z_vs_SMC 1 -42.072 1.5e-27 -7.681
DEMetro_Z_vs_SMC 2 -40.216 5.44e-27 -7.342
DEMetro_Z_vs_SMC 3 -88.123 8.74e-37 -16.089
DEMetro_Z_vs_SMC 4 0.191 0.85 0.035
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 6.357 9.489 17.780 -0.176
HMC 3.0 1.336 0.749 0.992 0.592
HMC 4.0 0.283 0.190 0.128 0.722
HMC 10.0 0.068 0.050 0.007 2.776
HMC 50.0 0.047 0.033 0.004 3.643
SMC 2.1 3060.211 9.489 17.780 171.585
SMC 3.0 304.990 0.749 0.992 306.734
SMC 4.0 188.910 0.190 0.128 1475.303
SMC 10.0 86.778 0.050 0.007 12818.266
SMC 50.0 6.641 0.033 0.004 1713.122
Metro 2.1 614.587 9.489 17.780 34.033
Metro 3.0 1.198 0.749 0.992 0.453
Metro 4.0 0.436 0.190 0.128 1.923
Metro 10.0 0.120 0.050 0.007 10.380
Metro 50.0 0.065 0.033 0.004 8.530
DEMetro_Z 2.1 993.734 9.489 17.780 55.358
DEMetro_Z 3.0 68.363 0.749 0.992 68.168
DEMetro_Z 4.0 39.710 0.190 0.128 308.941
DEMetro_Z 10.0 11.067 0.050 0.007 1628.366
DEMetro_Z 50.0 6.815 0.033 0.004 1758.242
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 5.508 5.6e-06 8.039
HMC 3.0 3.809 0.000666 13.667
HMC 4.0 4.749 4.71e-05 6.431
HMC 10.0 3.651 0.000598 1.130
HMC 50.0 1.658 0.103 0.399
SMC 2.1 411.458 1.98e-56 1456.165
SMC 3.0 396.793 8.3e-56 2330.328
SMC 4.0 287.941 1.04e-51 2802.889
SMC 10.0 215.657 4.78e-48 3605.540
SMC 50.0 78.550 2.34e-35 898.044
Metro 2.1 2.909 0.0069 94.373
Metro 3.0 9.016 5.96e-10 22.671
Metro 4.0 13.621 1.97e-14 17.479
Metro 10.0 21.292 4.73e-21 14.422
Metro 50.0 19.315 5.81e-21 9.967
DEMetro_Z 2.1 31.534 5.37e-24 760.442
DEMetro_Z 3.0 25.646 1.76e-21 950.354
DEMetro_Z 4.0 25.147 3.05e-21 1066.783
DEMetro_Z 10.0 25.412 2.28e-21 976.773
DEMetro_Z 50.0 15.458 1.54e-15 737.343
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -18.082 2.47e-17 -3.301
Metro_vs_DEMetro_Z 1 -24.765 4.67e-21 -4.521
Metro_vs_DEMetro_Z 2 -25.010 3.55e-21 -4.566
Metro_vs_DEMetro_Z 3 -24.895 4.03e-21 -4.545
Metro_vs_DEMetro_Z 4 -15.237 2.24e-15 -2.782
DEMetro_Z_vs_SMC 0 -30.109 1.98e-23 -5.497
DEMetro_Z_vs_SMC 1 -37.429 4.2e-26 -6.834
DEMetro_Z_vs_SMC 2 -37.033 5.69e-26 -6.761
DEMetro_Z_vs_SMC 3 -71.450 3.73e-34 -13.045
DEMetro_Z_vs_SMC 4 -3.253 0.0029 -0.594
HMC_vs_DEMetro_Z 0 -30.640 1.21e-23 -5.594
HMC_vs_DEMetro_Z 1 -25.797 1.5e-21 -4.710
HMC_vs_DEMetro_Z 2 -25.189 2.91e-21 -4.599
HMC_vs_DEMetro_Z 3 -25.302 2.57e-21 -4.619
HMC_vs_DEMetro_Z 4 -15.451 1.56e-15 -2.821
HMC_vs_Metro 0 -2.658 0.0127 -0.485
HMC_vs_Metro 1 -1.990 0.056 -0.363
HMC_vs_Metro 2 -5.947 1.84e-06 -1.086
HMC_vs_Metro 3 -21.232 3.23e-19 -3.876
HMC_vs_Metro 4 -19.365 3.93e-18 -3.536
HMC_vs_SMC 0 -324.356 3.55e-53 -59.219
HMC_vs_SMC 1 -331.172 1.94e-53 -60.463
HMC_vs_SMC 2 -280.645 2.36e-51 -51.239
HMC_vs_SMC 3 -215.143 5.23e-48 -39.280
HMC_vs_SMC 4 -78.561 2.41e-35 -14.343
Metro_vs_SMC 0 -41.364 2.44e-27 -7.552
Metro_vs_SMC 1 -403.779 6.2e-56 -73.720
Metro_vs_SMC 2 -288.990 1.01e-51 -52.762
Metro_vs_SMC 3 -210.827 9.42e-48 -38.492
Metro_vs_SMC 4 -77.608 3.43e-35 -14.169
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.353 0.118 0.029 8.039
HMC 3.0 0.140 0.065 0.005 13.667
HMC 4.0 0.072 0.050 0.004 6.431
HMC 10.0 0.036 0.034 0.002 1.130
HMC 50.0 0.030 0.029 0.002 0.399
SMC 2.1 42.600 0.118 0.029 1456.165
SMC 3.0 12.875 0.065 0.005 2330.328
SMC 4.0 9.996 0.050 0.004 2802.889
SMC 10.0 6.616 0.034 0.002 3605.540
SMC 50.0 1.402 0.029 0.002 898.044
Metro 2.1 2.871 0.118 0.029 94.373
Metro 3.0 0.190 0.065 0.005 22.671
Metro 4.0 0.112 0.050 0.004 17.479
Metro 10.0 0.060 0.034 0.002 14.422
Metro 50.0 0.045 0.029 0.002 9.967
DEMetro_Z 2.1 22.303 0.118 0.029 760.442
DEMetro_Z 3.0 5.289 0.065 0.005 950.354
DEMetro_Z 4.0 3.835 0.050 0.004 1066.783
DEMetro_Z 10.0 1.817 0.034 0.002 976.773
DEMetro_Z 50.0 1.156 0.029 0.002 737.343
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 5.269 1.2e-05 41.277
HMC 3.0 4.329 0.000161 15.287
HMC 4.0 4.387 0.000132 6.652
HMC 10.0 2.072 0.0428 0.589
HMC 50.0 0.145 0.885 0.034
SMC 2.1 222.478 2.03e-50 262.694
SMC 3.0 223.897 1.08e-50 252.788
SMC 4.0 239.733 2.06e-51 282.636
SMC 10.0 189.530 9.7e-48 266.335
SMC 50.0 190.984 1.57e-48 218.442
Metro 2.1 13.442 5.43e-14 148.206
Metro 3.0 9.054 5.54e-10 25.608
Metro 4.0 15.419 6.97e-16 19.140
Metro 10.0 20.655 5.29e-22 10.577
Metro 50.0 18.449 1.99e-21 8.021
DEMetro_Z 2.1 79.410 1.35e-35 314.895
DEMetro_Z 3.0 81.241 6.41e-36 283.466
DEMetro_Z 4.0 115.748 1.71e-40 320.607
DEMetro_Z 10.0 62.055 1.77e-32 270.040
DEMetro_Z 50.0 38.064 2.45e-26 257.261
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 12.041 8.35e-13 2.198
DEMetro_Z_vs_SMC 1 8.554 2.01e-09 1.562
DEMetro_Z_vs_SMC 2 12.265 5.32e-13 2.239
DEMetro_Z_vs_SMC 3 0.806 0.427 0.147
DEMetro_Z_vs_SMC 4 5.585 5e-06 1.020
HMC_vs_Metro 0 -7.668 1.87e-08 -1.400
HMC_vs_Metro 1 -2.096 0.0449 -0.383
HMC_vs_Metro 2 -5.613 4.62e-06 -1.025
HMC_vs_Metro 3 -21.209 3.33e-19 -3.872
HMC_vs_Metro 4 -19.528 3.13e-18 -3.565
Metro_vs_DEMetro_Z 0 -14.943 3.71e-15 -2.728
Metro_vs_DEMetro_Z 1 -51.750 4.01e-30 -9.448
Metro_vs_DEMetro_Z 2 -113.479 5.83e-40 -20.718
Metro_vs_DEMetro_Z 3 -57.252 2.2e-31 -10.453
Metro_vs_DEMetro_Z 4 -36.685 7.44e-26 -6.698
HMC_vs_SMC 0 -29.686 2.95e-23 -5.420
HMC_vs_SMC 1 -68.618 1.2e-33 -12.528
HMC_vs_SMC 2 -135.173 3.68e-42 -24.679
HMC_vs_SMC 3 -188.623 2.37e-46 -34.438
HMC_vs_SMC 4 -196.814 6.91e-47 -35.933
Metro_vs_SMC 0 -10.557 1.9e-11 -1.927
Metro_vs_SMC 1 -67.681 1.78e-33 -12.357
Metro_vs_SMC 2 -160.164 2.71e-44 -29.242
Metro_vs_SMC 3 -172.836 2.98e-45 -31.555
Metro_vs_SMC 4 -182.097 6.57e-46 -33.246
HMC_vs_DEMetro_Z 0 -31.432 5.91e-24 -5.739
HMC_vs_DEMetro_Z 1 -65.652 4.27e-33 -11.986
HMC_vs_DEMetro_Z 2 -108.202 2.31e-39 -19.755
HMC_vs_DEMetro_Z 3 -60.110 5.41e-32 -10.975
HMC_vs_DEMetro_Z 4 -38.101 2.54e-26 -6.956
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.077 0.015 0.001 41.277
HMC 3.0 0.039 0.015 0.002 15.287
HMC 4.0 0.024 0.015 0.001 6.652
HMC 10.0 0.015 0.014 0.001 0.589
HMC 50.0 0.014 0.014 0.001 0.034
SMC 2.1 0.409 0.015 0.001 262.694
SMC 3.0 0.406 0.015 0.002 252.788
SMC 4.0 0.399 0.015 0.001 282.636
SMC 10.0 0.398 0.014 0.001 266.335
SMC 50.0 0.307 0.014 0.001 218.442
Metro 2.1 0.237 0.015 0.001 148.206
Metro 3.0 0.055 0.015 0.002 25.608
Metro 4.0 0.041 0.015 0.001 19.140
Metro 10.0 0.029 0.014 0.001 10.577
Metro 50.0 0.025 0.014 0.001 8.021
DEMetro_Z 2.1 0.487 0.015 0.001 314.895
DEMetro_Z 3.0 0.453 0.015 0.002 283.466
DEMetro_Z 4.0 0.450 0.015 0.001 320.607
DEMetro_Z 10.0 0.403 0.014 0.001 270.040
DEMetro_Z 50.0 0.359 0.014 0.001 257.261
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.763 0.0881 2.965
HMC 3.0 0.844 0.404 0.438
HMC 4.0 -0.388 0.701 -0.272
HMC 10.0 -3.085 0.00319 -0.713
HMC 50.0 -3.755 0.000419 -0.876
SMC 2.1 35.799 5.64e-26 60.674
SMC 3.0 28.504 5.93e-23 65.762
SMC 4.0 23.092 2.61e-20 70.823
SMC 10.0 26.394 3.75e-22 45.541
SMC 50.0 23.375 6.98e-22 17.937
Metro 2.1 6.151 9.17e-07 8.726
Metro 3.0 14.775 2.02e-17 7.150
Metro 4.0 11.351 7.54e-13 8.657
Metro 10.0 18.007 8.5e-21 8.097
Metro 50.0 18.052 1.42e-22 6.617
DEMetro_Z 2.1 18.976 6.76e-18 347.184
DEMetro_Z 3.0 17.879 3.33e-17 359.552
DEMetro_Z 4.0 19.720 2.4e-18 409.903
DEMetro_Z 10.0 12.874 1.61e-13 304.126
DEMetro_Z 50.0 11.085 6.05e-12 209.480
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -19.248 4.63e-18 -3.514
HMC_vs_DEMetro_Z 1 -17.849 3.5e-17 -3.259
HMC_vs_DEMetro_Z 2 -19.931 1.8e-18 -3.639
HMC_vs_DEMetro_Z 3 -12.906 1.52e-13 -2.356
HMC_vs_DEMetro_Z 4 -11.164 5.13e-12 -2.038
Metro_vs_SMC 0 -21.521 2.23e-19 -3.929
Metro_vs_SMC 1 -23.920 1.22e-20 -4.367
Metro_vs_SMC 2 -23.574 1.82e-20 -4.304
Metro_vs_SMC 3 -21.576 2.08e-19 -3.939
Metro_vs_SMC 4 -13.353 6.48e-14 -2.438
Metro_vs_DEMetro_Z 0 -18.565 1.22e-17 -3.390
Metro_vs_DEMetro_Z 1 -17.624 4.91e-17 -3.218
Metro_vs_DEMetro_Z 2 -19.287 4.38e-18 -3.521
Metro_vs_DEMetro_Z 3 -12.507 3.3e-13 -2.283
Metro_vs_DEMetro_Z 4 -10.801 1.12e-11 -1.972
HMC_vs_Metro 0 -2.439 0.0211 -0.445
HMC_vs_Metro 1 -11.277 4.04e-12 -2.059
HMC_vs_Metro 2 -9.259 3.67e-10 -1.690
HMC_vs_Metro 3 -21.815 1.54e-19 -3.983
HMC_vs_Metro 4 -21.476 2.36e-19 -3.921
HMC_vs_SMC 0 -22.431 7.17e-20 -4.095
HMC_vs_SMC 1 -27.191 3.46e-22 -4.964
HMC_vs_SMC 2 -21.972 1.26e-19 -4.012
HMC_vs_SMC 3 -26.827 5.04e-22 -4.898
HMC_vs_SMC 4 -23.124 3.1e-20 -4.222
DEMetro_Z_vs_SMC 0 15.742 9.6e-16 2.874
DEMetro_Z_vs_SMC 1 14.131 1.55e-14 2.580
DEMetro_Z_vs_SMC 2 15.809 8.6e-16 2.886
DEMetro_Z_vs_SMC 3 10.853 9.98e-12 1.981
DEMetro_Z_vs_SMC 4 10.023 6.27e-11 1.830
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.136 0.070 0.022 2.965
HMC 3.0 0.041 0.038 0.005 0.438
HMC 4.0 0.031 0.032 0.004 -0.272
HMC 10.0 0.022 0.024 0.003 -0.713
HMC 50.0 0.020 0.022 0.003 -0.876
SMC 2.1 1.418 0.070 0.022 60.674
SMC 3.0 0.397 0.038 0.005 65.762
SMC 4.0 0.304 0.032 0.004 70.823
SMC 10.0 0.173 0.024 0.003 45.541
SMC 50.0 0.073 0.022 0.003 17.937
Metro 2.1 0.264 0.070 0.022 8.726
Metro 3.0 0.077 0.038 0.005 7.150
Metro 4.0 0.065 0.032 0.004 8.657
Metro 10.0 0.051 0.024 0.003 8.097
Metro 50.0 0.041 0.022 0.003 6.617
DEMetro_Z 2.1 7.785 0.070 0.022 347.184
DEMetro_Z 3.0 1.998 0.038 0.005 359.552
DEMetro_Z 4.0 1.603 0.032 0.004 409.903
DEMetro_Z 10.0 1.021 0.024 0.003 304.126
DEMetro_Z 50.0 0.618 0.022 0.003 209.480
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 0.632 0.532 0.404
HMC 3.0 0.034 0.973 0.007
HMC 4.0 2.044 0.0466 0.733
HMC 10.0 7.651 8.55e-10 2.754
HMC 50.0 10.548 9.46e-15 3.172
SMC 2.1 101.305 2.3e-39 160.489
SMC 3.0 158.780 6.81e-45 295.664
SMC 4.0 100.962 1.67e-38 1407.573
SMC 10.0 79.775 1.55e-35 11879.703
SMC 50.0 28.757 7.21e-23 1396.367
Metro 2.1 1.616 0.116 1.081
Metro 3.0 0.328 0.745 0.067
Metro 4.0 3.183 0.00324 2.618
Metro 10.0 13.293 7.28e-15 9.241
Metro 50.0 20.346 9.8e-23 9.126
DEMetro_Z 2.1 10.240 3.36e-11 24.122
DEMetro_Z 3.0 7.574 2.29e-08 24.815
DEMetro_Z 4.0 9.416 2.53e-10 112.138
DEMetro_Z 10.0 5.369 9.11e-06 630.386
DEMetro_Z 50.0 3.352 0.00225 396.386
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -90.220 4.43e-37 -16.472
HMC_vs_SMC 1 -160.399 2.59e-44 -29.285
HMC_vs_SMC 2 -101.243 1.58e-38 -18.484
HMC_vs_SMC 3 -79.774 1.55e-35 -14.565
HMC_vs_SMC 4 -28.664 7.9e-23 -5.233
Metro_vs_DEMetro_Z 0 -9.116 5.16e-10 -1.664
Metro_vs_DEMetro_Z 1 -7.569 2.41e-08 -1.382
Metro_vs_DEMetro_Z 2 -9.042 6.15e-10 -1.651
Metro_vs_DEMetro_Z 3 -5.285 1.15e-05 -0.965
Metro_vs_DEMetro_Z 4 -3.277 0.00272 -0.598
HMC_vs_Metro 0 -0.734 0.469 -0.134
HMC_vs_Metro 1 -0.387 0.702 -0.071
HMC_vs_Metro 2 -2.138 0.0411 -0.390
HMC_vs_Metro 3 -10.597 1.74e-11 -1.935
HMC_vs_Metro 4 -13.603 4.07e-14 -2.484
HMC_vs_DEMetro_Z 0 -10.841 1.02e-11 -1.979
HMC_vs_DEMetro_Z 1 -7.540 2.6e-08 -1.377
HMC_vs_DEMetro_Z 2 -9.361 2.89e-10 -1.709
HMC_vs_DEMetro_Z 3 -5.342 9.8e-06 -0.975
HMC_vs_DEMetro_Z 4 -3.326 0.0024 -0.607
Metro_vs_SMC 0 -85.623 2.01e-36 -15.633
Metro_vs_SMC 1 -157.415 4.47e-44 -28.740
Metro_vs_SMC 2 -100.771 1.81e-38 -18.398
Metro_vs_SMC 3 -79.720 1.58e-35 -14.555
Metro_vs_SMC 4 -28.585 8.53e-23 -5.219
DEMetro_Z_vs_SMC 0 -47.755 4.01e-29 -8.719
DEMetro_Z_vs_SMC 1 -63.609 1.06e-32 -11.613
DEMetro_Z_vs_SMC 2 -65.744 4.1e-33 -12.003
DEMetro_Z_vs_SMC 3 -52.722 2.35e-30 -9.626
DEMetro_Z_vs_SMC 4 -7.897 1.04e-08 -1.442
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 16.673 9.489 17.780 0.404
HMC 3.0 0.756 0.749 0.992 0.007
HMC 4.0 0.284 0.190 0.128 0.733
HMC 10.0 0.068 0.050 0.007 2.754
HMC 50.0 0.045 0.033 0.004 3.172
SMC 2.1 2862.923 9.489 17.780 160.489
SMC 3.0 294.010 0.749 0.992 295.664
SMC 4.0 180.246 0.190 0.128 1407.573
SMC 10.0 80.428 0.050 0.007 11879.703
SMC 50.0 5.419 0.033 0.004 1396.367
Metro 2.1 28.707 9.489 17.780 1.081
Metro 3.0 0.815 0.749 0.992 0.067
Metro 4.0 0.525 0.190 0.128 2.618
Metro 10.0 0.112 0.050 0.007 9.241
Metro 50.0 0.068 0.033 0.004 9.126
DEMetro_Z 2.1 438.374 9.489 17.780 24.122
DEMetro_Z 3.0 25.362 0.749 0.992 24.815
DEMetro_Z 4.0 14.535 0.190 0.128 112.138
DEMetro_Z 10.0 4.315 0.050 0.007 630.386
DEMetro_Z 50.0 1.562 0.033 0.004 396.386
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.663 0.107 19.157
HMC 3.0 3.991 0.000401 8.462
HMC 4.0 2.547 0.0163 5.306
HMC 10.0 3.284 0.00178 0.967
HMC 50.0 1.489 0.142 0.335
SMC 2.1 192.736 1.13e-46 1406.790
SMC 3.0 277.240 3.05e-51 2282.622
SMC 4.0 175.319 1.93e-45 2731.355
SMC 10.0 141.941 8.87e-43 3454.406
SMC 50.0 41.743 1.86e-27 780.220
Metro 2.1 4.000 0.000399 30.843
Metro 3.0 7.581 2.11e-08 15.683
Metro 4.0 7.585 2.11e-08 16.605
Metro 10.0 20.648 1.08e-20 13.765
Metro 50.0 21.887 4.82e-24 9.666
DEMetro_Z 2.1 19.490 3.29e-18 511.010
DEMetro_Z 3.0 14.741 5.26e-15 534.318
DEMetro_Z 4.0 17.332 7.63e-17 615.004
DEMetro_Z 10.0 13.177 9.03e-14 631.076
DEMetro_Z 50.0 10.597 1.74e-11 384.139
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -17.842 3.53e-17 -3.258
Metro_vs_DEMetro_Z 1 -14.248 1.26e-14 -2.601
Metro_vs_DEMetro_Z 2 -16.623 2.31e-16 -3.035
Metro_vs_DEMetro_Z 3 -12.855 1.67e-13 -2.347
Metro_vs_DEMetro_Z 4 -10.382 2.8e-11 -1.895
DEMetro_Z_vs_SMC 0 -32.867 1.68e-24 -6.001
DEMetro_Z_vs_SMC 1 -43.824 4.68e-28 -8.001
DEMetro_Z_vs_SMC 2 -51.540 4.5e-30 -9.410
DEMetro_Z_vs_SMC 3 -49.972 1.09e-29 -9.124
DEMetro_Z_vs_SMC 4 -9.418 2.52e-10 -1.720
HMC_vs_DEMetro_Z 0 -20.137 1.36e-18 -3.677
HMC_vs_DEMetro_Z 1 -14.523 7.71e-15 -2.651
HMC_vs_DEMetro_Z 2 -17.211 9.2e-17 -3.142
HMC_vs_DEMetro_Z 3 -13.163 9.28e-14 -2.403
HMC_vs_DEMetro_Z 4 -10.604 1.72e-11 -1.936
HMC_vs_Metro 0 -0.807 0.426 -0.147
HMC_vs_Metro 1 -2.253 0.032 -0.411
HMC_vs_Metro 2 -3.501 0.00152 -0.639
HMC_vs_Metro 3 -19.847 2.02e-18 -3.624
HMC_vs_Metro 4 -24.627 5.45e-21 -4.496
HMC_vs_SMC 0 -94.981 1e-37 -17.341
HMC_vs_SMC 1 -270.919 6.56e-51 -49.463
HMC_vs_SMC 2 -174.554 2.24e-45 -31.869
HMC_vs_SMC 3 -142.207 8.48e-43 -25.963
HMC_vs_SMC 4 -41.654 2e-27 -7.605
Metro_vs_SMC 0 -115.966 3.11e-40 -21.172
Metro_vs_SMC 1 -248.197 8.31e-50 -45.314
Metro_vs_SMC 2 -175.569 1.89e-45 -32.054
Metro_vs_SMC 3 -141.126 1.06e-42 -25.766
Metro_vs_SMC 4 -40.900 3.37e-27 -7.467
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.677 0.118 0.029 19.157
HMC 3.0 0.112 0.065 0.005 8.462
HMC 4.0 0.068 0.050 0.004 5.306
HMC 10.0 0.035 0.034 0.002 0.967
HMC 50.0 0.030 0.029 0.002 0.335
SMC 2.1 41.159 0.118 0.029 1406.790
SMC 3.0 12.612 0.065 0.005 2282.622
SMC 4.0 9.742 0.050 0.004 2731.355
SMC 10.0 6.340 0.034 0.002 3454.406
SMC 50.0 1.222 0.029 0.002 780.220
Metro 2.1 1.018 0.118 0.029 30.843
Metro 3.0 0.151 0.065 0.005 15.683
Metro 4.0 0.108 0.050 0.004 16.605
Metro 10.0 0.059 0.034 0.002 13.765
Metro 50.0 0.044 0.029 0.002 9.666
DEMetro_Z 2.1 15.026 0.118 0.029 511.010
DEMetro_Z 3.0 3.002 0.065 0.005 534.318
DEMetro_Z 4.0 2.232 0.050 0.004 615.004
DEMetro_Z 10.0 1.186 0.034 0.002 631.076
DEMetro_Z 50.0 0.616 0.029 0.002 384.139
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 3.242 0.00298 43.840
HMC 3.0 4.050 0.000343 9.114
HMC 4.0 2.718 0.0109 5.311
HMC 10.0 1.333 0.188 0.400
HMC 50.0 0.228 0.821 0.051
SMC 2.1 181.443 4.72e-47 267.347
SMC 3.0 257.151 3.02e-53 254.053
SMC 4.0 179.074 1.08e-46 287.756
SMC 10.0 204.776 6.13e-49 269.607
SMC 50.0 86.892 5.87e-37 204.820
Metro 2.1 7.851 1.17e-08 85.605
Metro 3.0 7.435 3.24e-08 20.963
Metro 4.0 10.049 4.52e-11 16.601
Metro 10.0 19.333 8.57e-21 10.300
Metro 50.0 19.950 1.25e-23 7.834
DEMetro_Z 2.1 52.346 2.66e-30 345.566
DEMetro_Z 3.0 45.455 1.52e-28 288.070
DEMetro_Z 4.0 41.322 2.39e-27 319.010
DEMetro_Z 10.0 24.657 5.17e-21 269.336
DEMetro_Z 50.0 18.241 1.93e-17 201.757
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 11.286 3.96e-12 2.061
DEMetro_Z_vs_SMC 1 5.468 6.91e-06 0.998
DEMetro_Z_vs_SMC 2 4.053 0.000347 0.740
DEMetro_Z_vs_SMC 3 -0.024 0.981 -0.004
DEMetro_Z_vs_SMC 4 -0.253 0.802 -0.046
HMC_vs_Metro 0 -2.598 0.0146 -0.474
HMC_vs_Metro 1 -3.004 0.00545 -0.548
HMC_vs_Metro 2 -4.130 0.000281 -0.754
HMC_vs_Metro 3 -19.468 3.4e-18 -3.554
HMC_vs_Metro 4 -22.279 8.64e-20 -4.068
Metro_vs_DEMetro_Z 0 -22.103 1.07e-19 -4.035
Metro_vs_DEMetro_Z 1 -35.713 1.6e-25 -6.520
Metro_vs_DEMetro_Z 2 -37.715 3.39e-26 -6.886
Metro_vs_DEMetro_Z 3 -23.560 1.85e-20 -4.302
Metro_vs_DEMetro_Z 4 -17.823 3.64e-17 -3.254
HMC_vs_SMC 0 -16.770 1.83e-16 -3.062
HMC_vs_SMC 1 -104.149 6.97e-39 -19.015
HMC_vs_SMC 2 -116.122 2.99e-40 -21.201
HMC_vs_SMC 3 -199.603 4.6e-47 -36.442
HMC_vs_SMC 4 -86.161 1.67e-36 -15.731
Metro_vs_SMC 0 -17.112 1.07e-16 -3.124
Metro_vs_SMC 1 -81.448 8.51e-36 -14.870
Metro_vs_SMC 2 -124.690 3.81e-41 -22.765
Metro_vs_SMC 3 -181.571 7.15e-46 -33.150
Metro_vs_SMC 4 -79.288 1.85e-35 -14.476
HMC_vs_DEMetro_Z 0 -21.037 4.15e-19 -3.841
HMC_vs_DEMetro_Z 1 -45.373 1.73e-28 -8.284
HMC_vs_DEMetro_Z 2 -47.618 4.36e-29 -8.694
HMC_vs_DEMetro_Z 3 -24.650 5.31e-21 -4.500
HMC_vs_DEMetro_Z 4 -18.278 1.85e-17 -3.337
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.081 0.015 0.001 43.840
HMC 3.0 0.029 0.015 0.002 9.114
HMC 4.0 0.022 0.015 0.001 5.311
HMC 10.0 0.015 0.014 0.001 0.400
HMC 50.0 0.014 0.014 0.001 0.051
SMC 2.1 0.416 0.015 0.001 267.347
SMC 3.0 0.408 0.015 0.002 254.053
SMC 4.0 0.406 0.015 0.001 287.756
SMC 10.0 0.402 0.014 0.001 269.607
SMC 50.0 0.289 0.014 0.001 204.820
Metro 2.1 0.143 0.015 0.001 85.605
Metro 3.0 0.048 0.015 0.002 20.963
Metro 4.0 0.037 0.015 0.001 16.601
Metro 10.0 0.029 0.014 0.001 10.300
Metro 50.0 0.024 0.014 0.001 7.834
DEMetro_Z 2.1 0.533 0.015 0.001 345.566
DEMetro_Z 3.0 0.460 0.015 0.002 288.070
DEMetro_Z 4.0 0.448 0.015 0.001 319.010
DEMetro_Z 10.0 0.402 0.014 0.001 269.336
DEMetro_Z 50.0 0.284 0.014 0.001 201.757
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Trace Plots
Pooled
2.1 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
4 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
50 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2.1 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
4 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
50 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2.1
3
4
10
50
Chain
2.1
3
4
10
50

Varying_Tails_with_high_Correlation (MvStudentT, nu, 30 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 1.462 0.15 0.456
HMC 3.0 4.335 8.6e-05 1.743
HMC 4.0 3.908 0.000399 2.216
HMC 10.0 3.901 0.000305 1.410
HMC 50.0 2.173 0.0349 0.801
SMC 2.1 2.392 0.0215 1.052
SMC 3.0 1.144 0.258 0.350
SMC 4.0 1.838 0.0718 0.582
SMC 10.0 -0.910 0.367 -0.213
SMC 50.0 -0.313 0.755 -0.082
Metro 2.1 5.171 8.64e-06 2.781
Metro 3.0 5.553 5.24e-06 13.031
Metro 4.0 6.272 6.8e-07 10.262
Metro 10.0 6.410 3.94e-07 6.695
Metro 50.0 5.628 3.21e-06 4.663
DEMetro_Z 2.1 3.481 0.00111 1.285
DEMetro_Z 3.0 4.813 3.53e-05 4.259
DEMetro_Z 4.0 4.420 9.24e-05 2.680
DEMetro_Z 10.0 3.449 0.00144 1.861
DEMetro_Z 50.0 2.223 0.0314 0.883
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -2.021 0.0525 -0.369
HMC_vs_DEMetro_Z 1 -2.773 0.00962 -0.506
HMC_vs_DEMetro_Z 2 -0.615 0.543 -0.112
HMC_vs_DEMetro_Z 3 -0.869 0.392 -0.159
HMC_vs_DEMetro_Z 4 -0.171 0.865 -0.031
Metro_vs_SMC 0 2.307 0.0284 0.421
Metro_vs_SMC 1 5.309 1.07e-05 0.969
Metro_vs_SMC 2 6.016 1.52e-06 1.098
Metro_vs_SMC 3 6.741 2.13e-07 1.231
Metro_vs_SMC 4 6.443 4.76e-07 1.176
Metro_vs_DEMetro_Z 0 2.565 0.0158 0.468
Metro_vs_DEMetro_Z 1 3.864 0.000577 0.706
Metro_vs_DEMetro_Z 2 4.204 0.00023 0.767
Metro_vs_DEMetro_Z 3 3.911 0.000509 0.714
Metro_vs_DEMetro_Z 4 4.497 0.000102 0.821
HMC_vs_Metro 0 -4.529 9.38e-05 -0.827
HMC_vs_Metro 1 -4.685 6.09e-05 -0.855
HMC_vs_Metro 2 -4.537 9.17e-05 -0.828
HMC_vs_Metro 3 -5.160 1.63e-05 -0.942
HMC_vs_Metro 4 -4.209 0.000226 -0.769
HMC_vs_SMC 0 -1.240 0.225 -0.226
HMC_vs_SMC 1 2.940 0.00638 0.537
HMC_vs_SMC 2 2.627 0.0136 0.480
HMC_vs_SMC 3 5.238 1.31e-05 0.956
HMC_vs_SMC 4 2.546 0.0165 0.465
DEMetro_Z_vs_SMC 0 0.471 0.641 0.086
DEMetro_Z_vs_SMC 1 4.339 0.000158 0.792
DEMetro_Z_vs_SMC 2 3.552 0.00133 0.649
DEMetro_Z_vs_SMC 3 3.856 0.00059 0.704
DEMetro_Z_vs_SMC 4 3.055 0.0048 0.558
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.082 0.062 0.044 0.456
HMC 3.0 0.055 0.027 0.016 1.743
HMC 4.0 0.050 0.022 0.013 2.216
HMC 10.0 0.036 0.019 0.013 1.410
HMC 50.0 0.030 0.021 0.012 0.801
SMC 2.1 0.109 0.062 0.044 1.052
SMC 3.0 0.033 0.027 0.016 0.350
SMC 4.0 0.029 0.022 0.013 0.582
SMC 10.0 0.016 0.019 0.013 -0.213
SMC 50.0 0.020 0.021 0.012 -0.082
Metro 2.1 0.184 0.062 0.044 2.781
Metro 3.0 0.233 0.027 0.016 13.031
Metro 4.0 0.152 0.022 0.013 10.262
Metro 10.0 0.103 0.019 0.013 6.695
Metro 50.0 0.077 0.021 0.012 4.663
DEMetro_Z 2.1 0.119 0.062 0.044 1.285
DEMetro_Z 3.0 0.094 0.027 0.016 4.259
DEMetro_Z 4.0 0.056 0.022 0.013 2.680
DEMetro_Z 10.0 0.042 0.019 0.013 1.861
DEMetro_Z 50.0 0.031 0.021 0.012 0.883
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -1.260 0.216 -0.245
HMC 3.0 2.051 0.0459 0.736
HMC 4.0 1.508 0.139 0.670
HMC 10.0 2.302 0.026 0.876
HMC 50.0 3.380 0.00152 1.301
SMC 2.1 2.547 0.0143 0.536
SMC 3.0 3.260 0.00206 1.149
SMC 4.0 -0.529 0.599 -0.149
SMC 10.0 -0.025 0.98 -0.007
SMC 50.0 -1.300 0.199 -0.343
Metro 2.1 -1.233 0.226 -0.234
Metro 3.0 2.490 0.0186 3.985
Metro 4.0 2.416 0.0222 6.658
Metro 10.0 5.160 1.12e-05 3.540
Metro 50.0 6.170 6.5e-07 4.948
DEMetro_Z 2.1 -1.590 0.122 -0.297
DEMetro_Z 3.0 3.918 0.000267 1.279
DEMetro_Z 4.0 3.274 0.00209 1.307
DEMetro_Z 10.0 4.425 7.59e-05 2.095
DEMetro_Z 50.0 4.154 0.00013 1.415
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -5.445 7.38e-06 -0.994
HMC_vs_SMC 1 -1.130 0.268 -0.206
HMC_vs_SMC 2 1.855 0.0738 0.339
HMC_vs_SMC 3 2.024 0.0523 0.370
HMC_vs_SMC 4 3.859 0.000586 0.705
Metro_vs_DEMetro_Z 0 1.877 0.0706 0.343
Metro_vs_DEMetro_Z 1 1.850 0.0745 0.338
Metro_vs_DEMetro_Z 2 1.954 0.0604 0.357
Metro_vs_DEMetro_Z 3 1.754 0.09 0.320
Metro_vs_DEMetro_Z 4 3.946 0.000463 0.721
HMC_vs_Metro 0 -0.180 0.858 -0.033
HMC_vs_Metro 1 -1.941 0.0621 -0.354
HMC_vs_Metro 2 -2.185 0.0371 -0.399
HMC_vs_Metro 3 -3.673 0.000963 -0.671
HMC_vs_Metro 4 -4.475 0.000109 -0.817
HMC_vs_DEMetro_Z 0 0.859 0.397 0.157
HMC_vs_DEMetro_Z 1 -1.344 0.189 -0.245
HMC_vs_DEMetro_Z 2 -1.139 0.264 -0.208
HMC_vs_DEMetro_Z 3 -2.270 0.0308 -0.415
HMC_vs_DEMetro_Z 4 -0.247 0.807 -0.045
Metro_vs_SMC 0 -6.009 1.56e-06 -1.097
Metro_vs_SMC 1 1.682 0.103 0.307
Metro_vs_SMC 2 2.428 0.0216 0.443
Metro_vs_SMC 3 5.257 1.24e-05 0.960
Metro_vs_SMC 4 6.438 4.82e-07 1.175
DEMetro_Z_vs_SMC 0 -6.841 1.63e-07 -1.249
DEMetro_Z_vs_SMC 1 0.321 0.75 0.059
DEMetro_Z_vs_SMC 2 3.887 0.000543 0.710
DEMetro_Z_vs_SMC 3 4.296 0.000178 0.784
DEMetro_Z_vs_SMC 4 5.445 7.37e-06 0.994
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 4.381 7.895 14.317 -0.245
HMC 3.0 0.614 0.368 0.335 0.736
HMC 4.0 0.206 0.147 0.088 0.670
HMC 10.0 0.069 0.045 0.027 0.876
HMC 50.0 0.049 0.028 0.016 1.301
SMC 2.1 15.567 7.895 14.317 0.536
SMC 3.0 0.753 0.368 0.335 1.149
SMC 4.0 0.134 0.147 0.088 -0.149
SMC 10.0 0.045 0.045 0.027 -0.007
SMC 50.0 0.023 0.028 0.016 -0.343
Metro 2.1 4.542 7.895 14.317 -0.234
Metro 3.0 1.701 0.368 0.335 3.985
Metro 4.0 0.731 0.147 0.088 6.658
Metro 10.0 0.141 0.045 0.027 3.540
Metro 50.0 0.106 0.028 0.016 4.948
DEMetro_Z 2.1 3.646 7.895 14.317 -0.297
DEMetro_Z 3.0 0.796 0.368 0.335 1.279
DEMetro_Z 4.0 0.261 0.147 0.088 1.307
DEMetro_Z 10.0 0.102 0.045 0.027 2.095
DEMetro_Z 50.0 0.051 0.028 0.016 1.415
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 2.652 0.011 0.994
HMC 3.0 6.850 3.09e-08 3.100
HMC 4.0 5.684 2.19e-06 3.629
HMC 10.0 4.818 2.06e-05 2.129
HMC 50.0 3.889 0.000308 1.357
SMC 2.1 12.165 4.57e-13 20.206
SMC 3.0 4.407 0.000112 3.788
SMC 4.0 1.024 0.31 0.316
SMC 10.0 0.230 0.819 0.060
SMC 50.0 -0.581 0.563 -0.143
Metro 2.1 10.670 4.49e-13 5.107
Metro 3.0 7.072 8.44e-08 20.043
Metro 4.0 7.982 7.7e-09 18.835
Metro 10.0 7.917 7.5e-09 10.357
Metro 50.0 6.731 1.55e-07 6.646
DEMetro_Z 2.1 7.363 6.52e-09 3.413
DEMetro_Z 3.0 9.230 1.87e-10 8.499
DEMetro_Z 4.0 10.589 1.04e-12 5.602
DEMetro_Z 10.0 7.465 8.41e-09 4.177
DEMetro_Z 50.0 5.400 2.16e-06 1.947
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 3.783 0.000719 0.691
Metro_vs_DEMetro_Z 1 4.293 0.000179 0.784
Metro_vs_DEMetro_Z 2 5.409 8.15e-06 0.987
Metro_vs_DEMetro_Z 3 4.274 0.000189 0.780
Metro_vs_DEMetro_Z 4 4.775 4.74e-05 0.872
DEMetro_Z_vs_SMC 0 -9.658 1.44e-10 -1.763
DEMetro_Z_vs_SMC 1 3.741 0.000804 0.683
DEMetro_Z_vs_SMC 2 9.185 4.38e-10 1.677
DEMetro_Z_vs_SMC 3 7.691 1.76e-08 1.404
DEMetro_Z_vs_SMC 4 7.623 2.1e-08 1.392
HMC_vs_DEMetro_Z 0 -4.430 0.000123 -0.809
HMC_vs_DEMetro_Z 1 -5.681 3.84e-06 -1.037
HMC_vs_DEMetro_Z 2 -2.575 0.0154 -0.470
HMC_vs_DEMetro_Z 3 -3.664 0.000988 -0.669
HMC_vs_DEMetro_Z 4 -1.243 0.224 -0.227
HMC_vs_Metro 0 -7.335 4.43e-08 -1.339
HMC_vs_Metro 1 -5.787 2.86e-06 -1.057
HMC_vs_Metro 2 -6.274 7.54e-07 -1.145
HMC_vs_Metro 3 -6.290 7.22e-07 -1.148
HMC_vs_Metro 4 -4.924 3.13e-05 -0.899
HMC_vs_SMC 0 -11.051 6.53e-12 -2.018
HMC_vs_SMC 1 -0.740 0.465 -0.135
HMC_vs_SMC 2 4.549 8.87e-05 0.831
HMC_vs_SMC 3 4.477 0.000108 0.817
HMC_vs_SMC 4 4.530 9.35e-05 0.827
Metro_vs_SMC 0 -8.527 2.15e-09 -1.557
Metro_vs_SMC 1 5.456 7.15e-06 0.996
Metro_vs_SMC 2 7.820 1.27e-08 1.428
Metro_vs_SMC 3 7.817 1.27e-08 1.427
Metro_vs_SMC 4 7.381 3.93e-08 1.348
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.157 0.118 0.039 0.994
HMC 3.0 0.091 0.060 0.010 3.100
HMC 4.0 0.072 0.043 0.008 3.629
HMC 10.0 0.048 0.031 0.008 2.129
HMC 50.0 0.041 0.029 0.008 1.357
SMC 2.1 0.914 0.118 0.039 20.206
SMC 3.0 0.099 0.060 0.010 3.788
SMC 4.0 0.045 0.043 0.008 0.316
SMC 10.0 0.031 0.031 0.008 0.060
SMC 50.0 0.028 0.029 0.008 -0.143
Metro 2.1 0.319 0.118 0.039 5.107
Metro 3.0 0.266 0.060 0.010 20.043
Metro 4.0 0.192 0.043 0.008 18.835
Metro 10.0 0.114 0.031 0.008 10.357
Metro 50.0 0.085 0.029 0.008 6.646
DEMetro_Z 2.1 0.253 0.118 0.039 3.413
DEMetro_Z 3.0 0.147 0.060 0.010 8.499
DEMetro_Z 4.0 0.087 0.043 0.008 5.602
DEMetro_Z 10.0 0.064 0.031 0.008 4.177
DEMetro_Z 50.0 0.046 0.029 0.008 1.947
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 4.293 8.73e-05 1.538
HMC 3.0 3.764 0.000468 1.368
HMC 4.0 5.793 1.11e-06 2.882
HMC 10.0 3.731 0.000562 1.536
HMC 50.0 3.830 0.000344 1.207
SMC 2.1 16.001 4.16e-16 29.239
SMC 3.0 4.532 6.81e-05 2.868
SMC 4.0 0.342 0.733 0.100
SMC 10.0 0.051 0.959 0.014
SMC 50.0 -0.562 0.576 -0.145
Metro 2.1 8.373 2.19e-09 10.127
Metro 3.0 10.259 1.53e-11 9.506
Metro 4.0 10.407 1.66e-11 13.385
Metro 10.0 8.028 4.62e-09 8.094
Metro 50.0 7.357 2.26e-08 5.975
DEMetro_Z 2.1 8.094 2.49e-09 5.893
DEMetro_Z 3.0 7.633 8.91e-09 5.548
DEMetro_Z 4.0 9.447 1.03e-11 4.297
DEMetro_Z 10.0 5.957 7.78e-07 3.255
DEMetro_Z 50.0 4.729 2.38e-05 1.870
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 -11.332 3.6e-12 -2.069
DEMetro_Z_vs_SMC 1 3.165 0.00363 0.578
DEMetro_Z_vs_SMC 2 8.208 4.75e-09 1.499
DEMetro_Z_vs_SMC 3 6.124 1.13e-06 1.118
DEMetro_Z_vs_SMC 4 6.518 3.88e-07 1.190
HMC_vs_Metro 0 -7.242 5.66e-08 -1.322
HMC_vs_Metro 1 -8.902 8.62e-10 -1.625
HMC_vs_Metro 2 -7.492 2.95e-08 -1.368
HMC_vs_Metro 3 -6.465 4.49e-07 -1.180
HMC_vs_Metro 4 -5.746 3.2e-06 -1.049
Metro_vs_DEMetro_Z 0 3.388 0.00204 0.619
Metro_vs_DEMetro_Z 1 3.257 0.00287 0.595
Metro_vs_DEMetro_Z 2 6.235 8.38e-07 1.138
Metro_vs_DEMetro_Z 3 4.279 0.000187 0.781
Metro_vs_DEMetro_Z 4 4.900 3.35e-05 0.895
HMC_vs_SMC 0 -14.581 6.96e-15 -2.662
HMC_vs_SMC 1 -2.145 0.0405 -0.392
HMC_vs_SMC 2 4.961 2.83e-05 0.906
HMC_vs_SMC 3 3.372 0.00213 0.616
HMC_vs_SMC 4 4.574 8.26e-05 0.835
Metro_vs_SMC 0 -8.522 2.17e-09 -1.556
Metro_vs_SMC 1 5.832 2.53e-06 1.065
Metro_vs_SMC 2 10.639 1.59e-11 1.942
Metro_vs_SMC 3 7.732 1.59e-08 1.412
Metro_vs_SMC 4 7.950 9.1e-09 1.451
HMC_vs_DEMetro_Z 0 -5.837 2.49e-06 -1.066
HMC_vs_DEMetro_Z 1 -5.103 1.91e-05 -0.932
HMC_vs_DEMetro_Z 2 -2.310 0.0282 -0.422
HMC_vs_DEMetro_Z 3 -2.763 0.00984 -0.504
HMC_vs_DEMetro_Z 4 -1.326 0.195 -0.242
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.023 0.015 0.006 1.538
HMC 3.0 0.021 0.015 0.005 1.368
HMC 4.0 0.023 0.013 0.004 2.882
HMC 10.0 0.021 0.014 0.005 1.536
HMC 50.0 0.021 0.015 0.005 1.207
SMC 2.1 0.177 0.015 0.006 29.239
SMC 3.0 0.028 0.015 0.005 2.868
SMC 4.0 0.013 0.013 0.004 0.100
SMC 10.0 0.014 0.014 0.005 0.014
SMC 50.0 0.014 0.015 0.005 -0.145
Metro 2.1 0.071 0.015 0.006 10.127
Metro 3.0 0.059 0.015 0.005 9.506
Metro 4.0 0.060 0.013 0.004 13.385
Metro 10.0 0.053 0.014 0.005 8.094
Metro 50.0 0.045 0.015 0.005 5.975
DEMetro_Z 2.1 0.047 0.015 0.006 5.893
DEMetro_Z 3.0 0.041 0.015 0.005 5.548
DEMetro_Z 4.0 0.028 0.013 0.004 4.297
DEMetro_Z 10.0 0.029 0.014 0.005 3.255
DEMetro_Z 50.0 0.024 0.015 0.005 1.870
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 0.341 0.734 0.099
HMC 3.0 4.887 2.01e-05 2.560
HMC 4.0 2.666 0.0112 1.331
HMC 10.0 2.225 0.0306 0.740
HMC 50.0 1.805 0.0771 0.598
SMC 2.1 3.260 0.00196 1.028
SMC 3.0 1.362 0.18 0.491
SMC 4.0 1.611 0.113 0.449
SMC 10.0 0.331 0.742 0.089
SMC 50.0 -1.217 0.228 -0.330
Metro 2.1 6.004 1.18e-06 5.684
Metro 3.0 6.578 2.78e-07 8.938
Metro 4.0 6.007 1.4e-06 9.391
Metro 10.0 4.930 2.64e-05 4.996
Metro 50.0 5.539 4.5e-06 5.344
DEMetro_Z 2.1 2.122 0.0394 0.811
DEMetro_Z 3.0 4.713 4.3e-05 3.390
DEMetro_Z 4.0 4.073 0.000248 2.327
DEMetro_Z 10.0 4.350 7.75e-05 1.658
DEMetro_Z 50.0 3.424 0.00143 1.531
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -1.793 0.0835 -0.327
HMC_vs_DEMetro_Z 1 -0.885 0.384 -0.162
HMC_vs_DEMetro_Z 2 -1.575 0.126 -0.288
HMC_vs_DEMetro_Z 3 -2.154 0.0396 -0.393
HMC_vs_DEMetro_Z 4 -2.041 0.0504 -0.373
Metro_vs_SMC 0 4.859 3.75e-05 0.887
Metro_vs_SMC 1 6.452 4.65e-07 1.178
Metro_vs_SMC 2 5.620 4.54e-06 1.026
Metro_vs_SMC 3 4.827 4.1e-05 0.881
Metro_vs_SMC 4 5.936 1.9e-06 1.084
Metro_vs_DEMetro_Z 0 5.261 1.23e-05 0.961
Metro_vs_DEMetro_Z 1 3.734 0.00082 0.682
Metro_vs_DEMetro_Z 2 4.385 0.00014 0.801
Metro_vs_DEMetro_Z 3 3.523 0.00143 0.643
Metro_vs_DEMetro_Z 4 3.884 0.000548 0.709
HMC_vs_Metro 0 -5.795 2.8e-06 -1.058
HMC_vs_Metro 1 -4.349 0.000154 -0.794
HMC_vs_Metro 2 -5.409 8.14e-06 -0.988
HMC_vs_Metro 3 -4.516 9.72e-05 -0.824
HMC_vs_Metro 4 -4.938 3.01e-05 -0.902
HMC_vs_SMC 0 -2.714 0.0111 -0.496
HMC_vs_SMC 1 3.714 0.000865 0.678
HMC_vs_SMC 2 1.814 0.0801 0.331
HMC_vs_SMC 3 2.036 0.0509 0.372
HMC_vs_SMC 4 2.606 0.0143 0.476
DEMetro_Z_vs_SMC 0 -0.476 0.638 -0.087
DEMetro_Z_vs_SMC 1 3.420 0.00188 0.624
DEMetro_Z_vs_SMC 2 3.743 0.000801 0.683
DEMetro_Z_vs_SMC 3 3.674 0.000962 0.671
DEMetro_Z_vs_SMC 4 4.079 0.000323 0.745
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.067 0.062 0.044 0.099
HMC 3.0 0.067 0.027 0.016 2.560
HMC 4.0 0.038 0.022 0.013 1.331
HMC 10.0 0.028 0.019 0.013 0.740
HMC 50.0 0.028 0.021 0.012 0.598
SMC 2.1 0.108 0.062 0.044 1.028
SMC 3.0 0.035 0.027 0.016 0.491
SMC 4.0 0.027 0.022 0.013 0.449
SMC 10.0 0.020 0.019 0.013 0.089
SMC 50.0 0.017 0.021 0.012 -0.330
Metro 2.1 0.312 0.062 0.044 5.684
Metro 3.0 0.168 0.027 0.016 8.938
Metro 4.0 0.141 0.022 0.013 9.391
Metro 10.0 0.081 0.019 0.013 4.996
Metro 50.0 0.085 0.021 0.012 5.344
DEMetro_Z 2.1 0.098 0.062 0.044 0.811
DEMetro_Z 3.0 0.081 0.027 0.016 3.390
DEMetro_Z 4.0 0.051 0.022 0.013 2.327
DEMetro_Z 10.0 0.040 0.019 0.013 1.658
DEMetro_Z 50.0 0.039 0.021 0.012 1.531
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -1.214 0.233 -0.233
HMC 3.0 1.267 0.215 2.130
HMC 4.0 1.883 0.065 0.544
HMC 10.0 3.068 0.00385 1.371
HMC 50.0 4.798 2.27e-05 2.180
SMC 2.1 0.318 0.752 0.066
SMC 3.0 2.664 0.0102 0.821
SMC 4.0 -0.160 0.873 -0.040
SMC 10.0 1.293 0.201 0.365
SMC 50.0 0.412 0.682 0.117
Metro 2.1 -1.347 0.187 -0.254
Metro 3.0 2.665 0.0103 0.865
Metro 4.0 5.177 1.15e-05 4.040
Metro 10.0 3.946 0.000389 2.783
Metro 50.0 4.083 0.000267 2.956
DEMetro_Z 2.1 -1.201 0.238 -0.227
DEMetro_Z 3.0 2.733 0.00838 0.779
DEMetro_Z 4.0 1.971 0.056 0.961
DEMetro_Z 10.0 2.941 0.00525 1.190
DEMetro_Z 50.0 2.047 0.0461 0.712
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 -2.666 0.0124 -0.487
HMC_vs_SMC 1 0.758 0.455 0.138
HMC_vs_SMC 2 2.049 0.0497 0.374
HMC_vs_SMC 3 2.086 0.0458 0.381
HMC_vs_SMC 4 4.159 0.000259 0.759
Metro_vs_DEMetro_Z 0 -1.176 0.249 -0.215
Metro_vs_DEMetro_Z 1 0.347 0.731 0.063
Metro_vs_DEMetro_Z 2 3.141 0.00386 0.573
Metro_vs_DEMetro_Z 3 2.139 0.041 0.390
Metro_vs_DEMetro_Z 4 2.860 0.00777 0.522
HMC_vs_Metro 0 0.545 0.59 0.100
HMC_vs_Metro 1 0.778 0.443 0.142
HMC_vs_Metro 2 -4.331 0.000162 -0.791
HMC_vs_Metro 3 -1.679 0.104 -0.306
HMC_vs_Metro 4 -1.065 0.296 -0.194
HMC_vs_DEMetro_Z 0 -0.145 0.885 -0.027
HMC_vs_DEMetro_Z 1 0.834 0.411 0.152
HMC_vs_DEMetro_Z 2 -0.753 0.458 -0.137
HMC_vs_DEMetro_Z 3 0.328 0.745 0.060
HMC_vs_DEMetro_Z 4 2.782 0.00939 0.508
Metro_vs_SMC 0 -2.978 0.00581 -0.544
Metro_vs_SMC 1 0.109 0.914 0.020
Metro_vs_SMC 2 5.176 1.55e-05 0.945
Metro_vs_SMC 3 3.300 0.00257 0.603
Metro_vs_SMC 4 4.251 0.000201 0.776
DEMetro_Z_vs_SMC 0 -2.857 0.00783 -0.522
DEMetro_Z_vs_SMC 1 -0.113 0.911 -0.021
DEMetro_Z_vs_SMC 2 2.024 0.0523 0.369
DEMetro_Z_vs_SMC 3 2.071 0.0474 0.378
DEMetro_Z_vs_SMC 4 1.509 0.142 0.276
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 4.558 7.895 14.317 -0.233
HMC 3.0 1.081 0.368 0.335 2.130
HMC 4.0 0.194 0.147 0.088 0.544
HMC 10.0 0.082 0.045 0.027 1.371
HMC 50.0 0.063 0.028 0.016 2.180
SMC 2.1 8.845 7.895 14.317 0.066
SMC 3.0 0.643 0.368 0.335 0.821
SMC 4.0 0.143 0.147 0.088 -0.040
SMC 10.0 0.055 0.045 0.027 0.365
SMC 50.0 0.030 0.028 0.016 0.117
Metro 2.1 4.264 7.895 14.317 -0.254
Metro 3.0 0.658 0.368 0.335 0.865
Metro 4.0 0.501 0.147 0.088 4.040
Metro 10.0 0.120 0.045 0.027 2.783
Metro 50.0 0.075 0.028 0.016 2.956
DEMetro_Z 2.1 4.641 7.895 14.317 -0.227
DEMetro_Z 3.0 0.629 0.368 0.335 0.779
DEMetro_Z 4.0 0.231 0.147 0.088 0.961
DEMetro_Z 10.0 0.077 0.045 0.027 1.190
DEMetro_Z 50.0 0.040 0.028 0.016 0.712
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 3.926 0.000275 1.377
HMC 3.0 6.360 2.75e-07 3.920
HMC 4.0 3.703 0.000718 2.107
HMC 10.0 5.111 6.05e-06 1.886
HMC 50.0 4.124 0.000147 1.438
SMC 2.1 6.018 1.41e-06 11.610
SMC 3.0 3.879 0.000401 1.885
SMC 4.0 0.313 0.755 0.094
SMC 10.0 1.729 0.0891 0.452
SMC 50.0 -0.975 0.334 -0.269
Metro 2.1 9.760 3.56e-11 7.531
Metro 3.0 10.288 2.36e-11 14.543
Metro 4.0 10.194 3.22e-11 16.594
Metro 10.0 6.652 2.22e-07 8.594
Metro 50.0 6.820 1.29e-07 7.495
DEMetro_Z 2.1 9.503 5.49e-13 2.995
DEMetro_Z 3.0 9.218 1.14e-10 6.481
DEMetro_Z 4.0 9.905 8.3e-12 5.515
DEMetro_Z 10.0 8.285 1.54e-10 3.226
DEMetro_Z 50.0 5.712 1.05e-06 2.408
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 5.959 1.78e-06 1.088
Metro_vs_DEMetro_Z 1 5.249 1.27e-05 0.958
Metro_vs_DEMetro_Z 2 6.597 3.14e-07 1.204
Metro_vs_DEMetro_Z 3 4.279 0.000187 0.781
Metro_vs_DEMetro_Z 4 4.435 0.000122 0.810
DEMetro_Z_vs_SMC 0 -4.462 0.000113 -0.815
DEMetro_Z_vs_SMC 1 6.262 7.78e-07 1.143
DEMetro_Z_vs_SMC 2 10.561 1.89e-11 1.928
DEMetro_Z_vs_SMC 3 6.862 1.55e-07 1.253
DEMetro_Z_vs_SMC 4 5.946 1.85e-06 1.086
HMC_vs_DEMetro_Z 0 -3.877 0.000558 -0.708
HMC_vs_DEMetro_Z 1 -2.647 0.013 -0.483
HMC_vs_DEMetro_Z 2 -4.357 0.00015 -0.796
HMC_vs_DEMetro_Z 3 -2.845 0.00806 -0.519
HMC_vs_DEMetro_Z 4 -2.057 0.0488 -0.376
HMC_vs_Metro 0 -7.442 3.35e-08 -1.359
HMC_vs_Metro 1 -7.187 6.54e-08 -1.312
HMC_vs_Metro 2 -9.383 2.74e-10 -1.713
HMC_vs_Metro 3 -5.347 9.68e-06 -0.976
HMC_vs_Metro 4 -5.352 9.54e-06 -0.977
HMC_vs_SMC 0 -5.235 1.32e-05 -0.956
HMC_vs_SMC 1 2.687 0.0118 0.491
HMC_vs_SMC 2 3.467 0.00166 0.633
HMC_vs_SMC 3 3.512 0.00148 0.641
HMC_vs_SMC 4 4.286 0.000183 0.783
Metro_vs_SMC 0 -1.791 0.0838 -0.327
Metro_vs_SMC 1 8.629 1.67e-09 1.575
Metro_vs_SMC 2 9.845 9.4e-11 1.797
Metro_vs_SMC 3 6.260 7.82e-07 1.143
Metro_vs_SMC 4 7.149 7.22e-08 1.305
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.172 0.118 0.039 1.377
HMC 3.0 0.100 0.060 0.010 3.920
HMC 4.0 0.060 0.043 0.008 2.107
HMC 10.0 0.046 0.031 0.008 1.886
HMC 50.0 0.041 0.029 0.008 1.438
SMC 2.1 0.575 0.118 0.039 11.610
SMC 3.0 0.079 0.060 0.010 1.885
SMC 4.0 0.044 0.043 0.008 0.094
SMC 10.0 0.034 0.031 0.008 0.452
SMC 50.0 0.027 0.029 0.008 -0.269
Metro 2.1 0.415 0.118 0.039 7.531
Metro 3.0 0.209 0.060 0.010 14.543
Metro 4.0 0.174 0.043 0.008 16.594
Metro 10.0 0.100 0.031 0.008 8.594
Metro 50.0 0.092 0.029 0.008 7.495
DEMetro_Z 2.1 0.236 0.118 0.039 2.995
DEMetro_Z 3.0 0.126 0.060 0.010 6.481
DEMetro_Z 4.0 0.086 0.043 0.008 5.515
DEMetro_Z 10.0 0.057 0.031 0.008 3.226
DEMetro_Z 50.0 0.050 0.029 0.008 2.408
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 5.184 4.55e-06 1.872
HMC 3.0 5.314 3.37e-06 2.068
HMC 4.0 3.289 0.00199 1.299
HMC 10.0 4.323 7.21e-05 1.419
HMC 50.0 4.034 0.000217 1.595
SMC 2.1 7.918 9.09e-09 19.116
SMC 3.0 2.994 0.00459 1.242
SMC 4.0 0.305 0.761 0.094
SMC 10.0 1.766 0.0828 0.490
SMC 50.0 -0.754 0.454 -0.214
Metro 2.1 9.720 6.03e-11 9.425
Metro 3.0 9.411 1.46e-10 10.114
Metro 4.0 12.195 2.63e-13 13.114
Metro 10.0 7.525 1.72e-08 7.296
Metro 50.0 7.418 2.01e-08 6.295
DEMetro_Z 2.1 8.868 6.48e-11 4.122
DEMetro_Z 3.0 7.592 3.32e-09 3.558
DEMetro_Z 4.0 8.876 1.27e-10 4.825
DEMetro_Z 10.0 5.921 4.93e-07 2.424
DEMetro_Z 50.0 4.650 3.2e-05 1.898
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 -6.254 7.96e-07 -1.142
DEMetro_Z_vs_SMC 1 5.564 5.3e-06 1.016
DEMetro_Z_vs_SMC 2 10.077 5.54e-11 1.840
DEMetro_Z_vs_SMC 3 4.404 0.000132 0.804
DEMetro_Z_vs_SMC 4 4.557 8.67e-05 0.832
HMC_vs_Metro 0 -7.950 9.1e-09 -1.451
HMC_vs_Metro 1 -7.682 1.8e-08 -1.403
HMC_vs_Metro 2 -10.486 2.22e-11 -1.915
HMC_vs_Metro 3 -5.965 1.76e-06 -1.089
HMC_vs_Metro 4 -5.369 9.11e-06 -0.980
Metro_vs_DEMetro_Z 0 4.687 6.06e-05 0.856
Metro_vs_DEMetro_Z 1 6.464 4.5e-07 1.180
Metro_vs_DEMetro_Z 2 7.770 1.44e-08 1.419
Metro_vs_DEMetro_Z 3 4.925 3.13e-05 0.899
Metro_vs_DEMetro_Z 4 4.578 8.18e-05 0.836
HMC_vs_SMC 0 -7.322 4.59e-08 -1.337
HMC_vs_SMC 1 1.777 0.0861 0.324
HMC_vs_SMC 2 2.997 0.00554 0.547
HMC_vs_SMC 3 2.557 0.016 0.467
HMC_vs_SMC 4 3.916 0.000502 0.715
Metro_vs_SMC 0 -3.623 0.0011 -0.661
Metro_vs_SMC 1 8.075 6.63e-09 1.474
Metro_vs_SMC 2 11.879 1.16e-12 2.169
Metro_vs_SMC 3 7.148 7.23e-08 1.305
Metro_vs_SMC 4 7.670 1.86e-08 1.400
HMC_vs_DEMetro_Z 0 -3.958 0.000449 -0.723
HMC_vs_DEMetro_Z 1 -2.655 0.0128 -0.485
HMC_vs_DEMetro_Z 2 -5.794 2.81e-06 -1.058
HMC_vs_DEMetro_Z 3 -2.160 0.0391 -0.394
HMC_vs_DEMetro_Z 4 -0.588 0.561 -0.107
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.025 0.015 0.006 1.872
HMC 3.0 0.024 0.015 0.005 2.068
HMC 4.0 0.017 0.013 0.004 1.299
HMC 10.0 0.021 0.014 0.005 1.419
HMC 50.0 0.023 0.015 0.005 1.595
SMC 2.1 0.121 0.015 0.006 19.116
SMC 3.0 0.020 0.015 0.005 1.242
SMC 4.0 0.013 0.013 0.004 0.094
SMC 10.0 0.016 0.014 0.005 0.490
SMC 50.0 0.014 0.015 0.005 -0.214
Metro 2.1 0.067 0.015 0.006 9.425
Metro 3.0 0.062 0.015 0.005 10.114
Metro 4.0 0.059 0.013 0.004 13.114
Metro 10.0 0.049 0.014 0.005 7.296
Metro 50.0 0.046 0.015 0.005 6.295
DEMetro_Z 2.1 0.038 0.015 0.006 4.122
DEMetro_Z 3.0 0.031 0.015 0.005 3.558
DEMetro_Z 4.0 0.030 0.013 0.004 4.825
DEMetro_Z 10.0 0.025 0.014 0.005 2.424
DEMetro_Z 50.0 0.024 0.015 0.005 1.898
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Trace Plots
Pooled
2.1 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
4 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
50 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2.1 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
4 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
50 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2.1
3
4
10
50
Chain
2.1
3
4
10
50

Vary_Tails_with_high_Multimodality (Mixture, nu, 30 runs)

Pooled Chains results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 7.831 9.93e-09 11.492
HMC 3.0 5.572 4.95e-06 12.373
HMC 4.0 8.188 4.66e-09 22.303
HMC 10.0 5.170 1.56e-05 18.164
HMC 50.0 5.818 2.6e-06 32.462
SMC 2.1 6.532 3.12e-07 8.659
SMC 3.0 3.921 0.00031 1.570
SMC 4.0 1.639 0.107 0.509
SMC 10.0 0.185 0.854 0.043
SMC 50.0 1.362 0.179 0.377
Metro 2.1 6.265 2.9e-07 3.348
Metro 3.0 7.002 7.57e-08 7.286
Metro 4.0 6.372 5.6e-07 19.726
Metro 10.0 4.790 4.51e-05 19.764
Metro 50.0 5.736 3.27e-06 34.029
DEMetro_Z 2.1 8.206 4.3e-09 18.141
DEMetro_Z 3.0 6.392 4.94e-07 11.036
DEMetro_Z 4.0 8.718 1.3e-09 33.768
DEMetro_Z 10.0 6.373 5.61e-07 22.497
DEMetro_Z 50.0 7.023 9.93e-08 35.491
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -2.192 0.0366 -0.400
HMC_vs_DEMetro_Z 1 0.529 0.601 0.097
HMC_vs_DEMetro_Z 2 -2.347 0.026 -0.429
HMC_vs_DEMetro_Z 3 -0.846 0.404 -0.154
HMC_vs_DEMetro_Z 4 -0.419 0.678 -0.077
Metro_vs_SMC 0 -3.648 0.00103 -0.666
Metro_vs_SMC 1 5.277 1.18e-05 0.963
Metro_vs_SMC 2 6.098 1.22e-06 1.113
Metro_vs_SMC 3 4.780 4.67e-05 0.873
Metro_vs_SMC 4 5.718 3.46e-06 1.044
Metro_vs_DEMetro_Z 0 -6.745 2.11e-07 -1.231
Metro_vs_DEMetro_Z 1 -1.844 0.0754 -0.337
Metro_vs_DEMetro_Z 2 -2.858 0.0078 -0.522
Metro_vs_DEMetro_Z 3 -0.441 0.662 -0.081
Metro_vs_DEMetro_Z 4 -0.198 0.845 -0.036
HMC_vs_Metro 0 5.114 1.85e-05 0.934
HMC_vs_Metro 1 1.978 0.0575 0.361
HMC_vs_Metro 2 0.597 0.555 0.109
HMC_vs_Metro 3 -0.350 0.729 -0.064
HMC_vs_Metro 4 -0.330 0.744 -0.060
HMC_vs_SMC 0 1.359 0.185 0.248
HMC_vs_SMC 1 4.774 4.75e-05 0.872
HMC_vs_SMC 2 7.818 1.27e-08 1.427
HMC_vs_SMC 3 5.124 1.8e-05 0.935
HMC_vs_SMC 4 5.801 2.76e-06 1.059
DEMetro_Z_vs_SMC 0 3.979 0.000423 0.727
DEMetro_Z_vs_SMC 1 5.477 6.75e-06 1.000
DEMetro_Z_vs_SMC 2 8.512 2.23e-09 1.554
DEMetro_Z_vs_SMC 3 6.343 6.24e-07 1.158
DEMetro_Z_vs_SMC 4 7.031 9.87e-08 1.284
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.940 0.101 0.073 11.492
HMC 3.0 1.288 0.129 0.094 12.373
HMC 4.0 1.638 0.097 0.069 22.303
HMC 10.0 1.544 0.088 0.080 18.164
HMC 50.0 2.026 0.087 0.060 32.462
SMC 2.1 0.733 0.101 0.073 8.659
SMC 3.0 0.276 0.129 0.094 1.570
SMC 4.0 0.132 0.097 0.069 0.509
SMC 10.0 0.091 0.088 0.080 0.043
SMC 50.0 0.110 0.087 0.060 0.377
Metro 2.1 0.345 0.101 0.073 3.348
Metro 3.0 0.811 0.129 0.094 7.286
Metro 4.0 1.460 0.097 0.069 19.726
Metro 10.0 1.672 0.088 0.080 19.764
Metro 50.0 2.120 0.087 0.060 34.029
DEMetro_Z 2.1 1.425 0.101 0.073 18.141
DEMetro_Z 3.0 1.163 0.129 0.094 11.036
DEMetro_Z 4.0 2.431 0.097 0.069 33.768
DEMetro_Z 10.0 1.891 0.088 0.080 22.497
DEMetro_Z 50.0 2.207 0.087 0.060 35.491
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -1.300 0.203 -0.239
HMC 3.0 2.502 0.0166 1.159
HMC 4.0 4.034 0.000364 23.406
HMC 10.0 3.891 0.000537 39.467
HMC 50.0 4.223 0.000218 62.604
SMC 2.1 -1.341 0.19 -0.246
SMC 3.0 -1.497 0.145 -0.275
SMC 4.0 -0.936 0.353 -0.232
SMC 10.0 -0.520 0.605 -0.131
SMC 50.0 -1.769 0.0825 -0.408
Metro 2.1 -1.357 0.185 -0.250
Metro 3.0 1.646 0.106 0.350
Metro 4.0 3.258 0.00286 22.126
Metro 10.0 3.510 0.00148 52.079
Metro 50.0 4.257 0.000198 70.022
DEMetro_Z 2.1 -0.866 0.393 -0.160
DEMetro_Z 3.0 2.723 0.00868 0.812
DEMetro_Z 4.0 4.826 4.11e-05 50.166
DEMetro_Z 10.0 3.883 0.000549 49.977
DEMetro_Z 50.0 4.758 4.97e-05 64.169
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 0.275 0.786 0.050
HMC_vs_SMC 1 3.377 0.0021 0.617
HMC_vs_SMC 2 4.067 0.000334 0.742
HMC_vs_SMC 3 3.936 0.000476 0.719
HMC_vs_SMC 4 4.242 0.000207 0.775
Metro_vs_DEMetro_Z 0 -4.048 0.000351 -0.739
Metro_vs_DEMetro_Z 1 -1.643 0.111 -0.300
Metro_vs_DEMetro_Z 2 -2.212 0.035 -0.404
Metro_vs_DEMetro_Z 3 0.095 0.925 0.017
Metro_vs_DEMetro_Z 4 0.288 0.776 0.053
HMC_vs_Metro 0 0.459 0.649 0.084
HMC_vs_Metro 1 1.824 0.0784 0.333
HMC_vs_Metro 2 0.130 0.897 0.024
HMC_vs_Metro 3 -0.755 0.456 -0.138
HMC_vs_Metro 4 -0.542 0.592 -0.099
HMC_vs_DEMetro_Z 0 -2.568 0.0157 -0.469
HMC_vs_DEMetro_Z 1 0.751 0.458 0.137
HMC_vs_DEMetro_Z 2 -2.153 0.0397 -0.393
HMC_vs_DEMetro_Z 3 -0.622 0.539 -0.114
HMC_vs_DEMetro_Z 4 -0.086 0.932 -0.016
Metro_vs_SMC 0 -0.159 0.875 -0.029
Metro_vs_SMC 1 5.432 7.63e-06 0.992
Metro_vs_SMC 2 3.282 0.00269 0.599
Metro_vs_SMC 3 3.521 0.00144 0.643
Metro_vs_SMC 4 4.279 0.000187 0.781
DEMetro_Z_vs_SMC 0 2.867 0.00765 0.523
DEMetro_Z_vs_SMC 1 4.546 8.95e-05 0.830
DEMetro_Z_vs_SMC 2 4.826 4.12e-05 0.881
DEMetro_Z_vs_SMC 3 3.888 0.000542 0.710
DEMetro_Z_vs_SMC 4 4.784 4.62e-05 0.873
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 5.044 13.069 33.570 -0.239
HMC 3.0 4.336 1.344 2.582 1.159
HMC 4.0 5.305 0.388 0.210 23.406
HMC 10.0 6.701 0.212 0.164 39.467
HMC 50.0 10.237 0.226 0.160 62.604
SMC 2.1 4.823 13.069 33.570 -0.246
SMC 3.0 0.633 1.344 2.582 -0.275
SMC 4.0 0.340 0.388 0.210 -0.232
SMC 10.0 0.190 0.212 0.164 -0.131
SMC 50.0 0.161 0.226 0.160 -0.408
Metro 2.1 4.680 13.069 33.570 -0.250
Metro 3.0 2.248 1.344 2.582 0.350
Metro 4.0 5.036 0.388 0.210 22.126
Metro 10.0 8.775 0.212 0.164 52.079
Metro 50.0 11.423 0.226 0.160 70.022
DEMetro_Z 2.1 7.691 13.069 33.570 -0.160
DEMetro_Z 3.0 3.441 1.344 2.582 0.812
DEMetro_Z 4.0 10.926 0.388 0.210 50.166
DEMetro_Z 10.0 8.430 0.212 0.164 49.977
DEMetro_Z 50.0 10.487 0.226 0.160 64.169
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 7.930 7.03e-09 9.872
HMC 3.0 5.733 3.2e-06 14.648
HMC 4.0 7.822 1.2e-08 24.159
HMC 10.0 5.121 1.79e-05 20.015
HMC 50.0 5.782 2.88e-06 35.147
SMC 2.1 7.989 5.68e-09 9.089
SMC 3.0 5.523 1.82e-06 2.244
SMC 4.0 1.966 0.0547 0.634
SMC 10.0 0.164 0.871 0.037
SMC 50.0 1.235 0.222 0.347
Metro 2.1 7.802 1.61e-09 3.591
Metro 3.0 7.319 3.47e-08 8.727
Metro 4.0 6.583 3.17e-07 21.873
Metro 10.0 4.722 5.45e-05 21.812
Metro 50.0 5.815 2.64e-06 37.080
DEMetro_Z 2.1 8.691 1.23e-09 16.339
DEMetro_Z 3.0 6.606 2.83e-07 13.292
DEMetro_Z 4.0 9.047 5.87e-10 36.830
DEMetro_Z 10.0 6.577 3.24e-07 24.262
DEMetro_Z 50.0 6.949 1.21e-07 38.621
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -6.819 1.73e-07 -1.245
Metro_vs_DEMetro_Z 1 -1.975 0.0578 -0.361
Metro_vs_DEMetro_Z 2 -2.856 0.00786 -0.521
Metro_vs_DEMetro_Z 3 -0.364 0.718 -0.067
Metro_vs_DEMetro_Z 4 -0.193 0.849 -0.035
DEMetro_Z_vs_SMC 0 3.605 0.00115 0.658
DEMetro_Z_vs_SMC 1 5.415 8.01e-06 0.989
DEMetro_Z_vs_SMC 2 8.808 1.08e-09 1.608
DEMetro_Z_vs_SMC 3 6.527 3.79e-07 1.192
DEMetro_Z_vs_SMC 4 6.955 1.21e-07 1.270
HMC_vs_DEMetro_Z 0 -2.544 0.0166 -0.464
HMC_vs_DEMetro_Z 1 0.476 0.638 0.087
HMC_vs_DEMetro_Z 2 -2.409 0.0226 -0.440
HMC_vs_DEMetro_Z 3 -0.772 0.446 -0.141
HMC_vs_DEMetro_Z 4 -0.441 0.662 -0.081
HMC_vs_Metro 0 4.664 6.45e-05 0.851
HMC_vs_Metro 1 2.011 0.0537 0.367
HMC_vs_Metro 2 0.471 0.641 0.086
HMC_vs_Metro 3 -0.348 0.73 -0.064
HMC_vs_Metro 4 -0.380 0.707 -0.069
HMC_vs_SMC 0 0.434 0.667 0.079
HMC_vs_SMC 1 4.775 4.74e-05 0.872
HMC_vs_SMC 2 7.487 2.98e-08 1.367
HMC_vs_SMC 3 5.089 1.98e-05 0.929
HMC_vs_SMC 4 5.768 3.02e-06 1.053
Metro_vs_SMC 0 -4.471 0.00011 -0.816
Metro_vs_SMC 1 5.295 1.12e-05 0.967
Metro_vs_SMC 2 6.269 7.64e-07 1.144
Metro_vs_SMC 3 4.723 5.47e-05 0.862
Metro_vs_SMC 4 5.801 2.75e-06 1.059
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.919 0.179 0.075 9.872
HMC 3.0 1.170 0.156 0.069 14.648
HMC 4.0 1.480 0.118 0.056 24.159
HMC 10.0 1.437 0.101 0.067 20.015
HMC 50.0 1.843 0.099 0.050 35.147
SMC 2.1 0.860 0.179 0.075 9.089
SMC 3.0 0.311 0.156 0.069 2.244
SMC 4.0 0.153 0.118 0.056 0.634
SMC 10.0 0.103 0.101 0.067 0.037
SMC 50.0 0.116 0.099 0.050 0.347
Metro 2.1 0.448 0.179 0.075 3.591
Metro 3.0 0.760 0.156 0.069 8.727
Metro 4.0 1.351 0.118 0.056 21.873
Metro 10.0 1.557 0.101 0.067 21.812
Metro 50.0 1.939 0.099 0.050 37.080
DEMetro_Z 2.1 1.403 0.179 0.075 16.339
DEMetro_Z 3.0 1.076 0.156 0.069 13.292
DEMetro_Z 4.0 2.195 0.118 0.056 36.830
DEMetro_Z 10.0 1.721 0.101 0.067 24.262
DEMetro_Z 50.0 2.016 0.099 0.050 38.621
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 7.636 1.78e-08 14.077
HMC 3.0 5.296 1.09e-05 14.974
HMC 4.0 8.008 7.47e-09 25.181
HMC 10.0 5.247 1.26e-05 19.667
HMC 50.0 5.933 1.9e-06 37.328
SMC 2.1 6.520 3.46e-07 11.010
SMC 3.0 4.162 0.000156 1.780
SMC 4.0 1.458 0.151 0.452
SMC 10.0 0.079 0.937 0.018
SMC 50.0 1.092 0.279 0.293
Metro 2.1 6.831 6.85e-08 4.238
Metro 3.0 6.443 3.97e-07 8.399
Metro 4.0 6.411 5.05e-07 21.671
Metro 10.0 4.945 2.93e-05 21.456
Metro 50.0 5.862 2.32e-06 38.577
DEMetro_Z 2.1 7.654 1.85e-08 24.051
DEMetro_Z 3.0 6.107 1.12e-06 13.219
DEMetro_Z 4.0 8.868 9.06e-10 37.501
DEMetro_Z 10.0 6.486 4.15e-07 24.500
DEMetro_Z 50.0 7.227 5.81e-08 40.164
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 3.987 0.000415 0.728
DEMetro_Z_vs_SMC 1 5.277 1.17e-05 0.964
DEMetro_Z_vs_SMC 2 8.684 1.46e-09 1.586
DEMetro_Z_vs_SMC 3 6.459 4.56e-07 1.179
DEMetro_Z_vs_SMC 4 7.239 5.69e-08 1.322
HMC_vs_Metro 0 5.029 2.34e-05 0.918
HMC_vs_Metro 1 1.983 0.0569 0.362
HMC_vs_Metro 2 0.717 0.479 0.131
HMC_vs_Metro 3 -0.372 0.713 -0.068
HMC_vs_Metro 4 -0.234 0.816 -0.043
Metro_vs_DEMetro_Z 0 -6.109 1.18e-06 -1.115
Metro_vs_DEMetro_Z 1 -1.890 0.0688 -0.345
Metro_vs_DEMetro_Z 2 -2.956 0.00613 -0.540
Metro_vs_DEMetro_Z 3 -0.465 0.645 -0.085
Metro_vs_DEMetro_Z 4 -0.193 0.848 -0.035
HMC_vs_SMC 0 1.145 0.262 0.209
HMC_vs_SMC 1 4.586 8e-05 0.837
HMC_vs_SMC 2 7.718 1.65e-08 1.409
HMC_vs_SMC 3 5.222 1.37e-05 0.953
HMC_vs_SMC 4 5.925 1.96e-06 1.082
Metro_vs_SMC 0 -3.572 0.00126 -0.652
Metro_vs_SMC 1 4.957 2.86e-05 0.905
Metro_vs_SMC 2 6.170 9.99e-07 1.127
Metro_vs_SMC 3 4.942 2.98e-05 0.902
Metro_vs_SMC 4 5.857 2.36e-06 1.069
HMC_vs_DEMetro_Z 0 -2.404 0.0228 -0.439
HMC_vs_DEMetro_Z 1 0.561 0.579 0.102
HMC_vs_DEMetro_Z 2 -2.256 0.0318 -0.412
HMC_vs_DEMetro_Z 3 -0.884 0.384 -0.161
HMC_vs_DEMetro_Z 4 -0.347 0.731 -0.063
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.094 0.010 0.006 14.077
HMC 3.0 0.143 0.014 0.009 14.974
HMC 4.0 0.189 0.011 0.007 25.181
HMC 10.0 0.176 0.010 0.008 19.667
HMC 50.0 0.231 0.009 0.006 37.328
SMC 2.1 0.075 0.010 0.006 11.010
SMC 3.0 0.029 0.014 0.009 1.780
SMC 4.0 0.014 0.011 0.007 0.452
SMC 10.0 0.010 0.010 0.008 0.018
SMC 50.0 0.011 0.009 0.006 0.293
Metro 2.1 0.035 0.010 0.006 4.238
Metro 3.0 0.086 0.014 0.009 8.399
Metro 4.0 0.164 0.011 0.007 21.671
Metro 10.0 0.191 0.010 0.008 21.456
Metro 50.0 0.239 0.009 0.006 38.577
DEMetro_Z 2.1 0.153 0.010 0.006 24.051
DEMetro_Z 3.0 0.128 0.014 0.009 13.219
DEMetro_Z 4.0 0.276 0.011 0.007 37.501
DEMetro_Z 10.0 0.217 0.010 0.008 24.500
DEMetro_Z 50.0 0.248 0.009 0.006 40.164
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
R Hat (scatter)
Mode Transitions
mode_transitions plot
One Chain results
Mean Rmse
mean_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 5.901 1.86e-06 8.655
HMC 3.0 7.185 5.8e-08 12.725
HMC 4.0 6.372 5.65e-07 23.935
HMC 10.0 34.424 2.22e-25 67.200
HMC 50.0 290.319 1.55e-84 93.216
SMC 2.1 6.815 1.49e-07 10.083
SMC 3.0 2.860 0.00664 1.244
SMC 4.0 1.705 0.0936 0.449
SMC 10.0 0.027 0.979 0.006
SMC 50.0 1.179 0.243 0.325
Metro 2.1 4.548 6.93e-05 3.260
Metro 3.0 4.445 0.000107 4.899
Metro 4.0 4.544 8.95e-05 26.049
Metro 10.0 13.097 9.94e-14 57.467
Metro 50.0 42.159 7.31e-28 91.118
DEMetro_Z 2.1 5.049 2.2e-05 23.919
DEMetro_Z 3.0 5.797 2.65e-06 12.711
DEMetro_Z 4.0 4.873 3.59e-05 28.312
DEMetro_Z 10.0 11.959 9.45e-13 56.954
DEMetro_Z 50.0 13.312 6.78e-14 78.965
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_DEMetro_Z 0 -3.000 0.00549 -0.548
HMC_vs_DEMetro_Z 1 0.005 0.996 0.001
HMC_vs_DEMetro_Z 2 -0.687 0.497 -0.126
HMC_vs_DEMetro_Z 3 1.902 0.0672 0.347
HMC_vs_DEMetro_Z 4 2.380 0.0241 0.434
Metro_vs_SMC 0 -4.328 0.000163 -0.790
Metro_vs_SMC 1 2.832 0.00832 0.517
Metro_vs_SMC 2 4.505 0.0001 0.823
Metro_vs_SMC 3 13.228 8.19e-14 2.415
Metro_vs_SMC 4 42.297 1.29e-27 7.722
Metro_vs_DEMetro_Z 0 -4.383 0.00014 -0.800
Metro_vs_DEMetro_Z 1 -3.048 0.00487 -0.557
Metro_vs_DEMetro_Z 2 -0.309 0.759 -0.056
Metro_vs_DEMetro_Z 3 0.102 0.92 0.019
Metro_vs_DEMetro_Z 4 1.859 0.0732 0.339
HMC_vs_Metro 0 3.243 0.00297 0.592
HMC_vs_Metro 1 3.456 0.00171 0.631
HMC_vs_Metro 2 -0.306 0.762 -0.056
HMC_vs_Metro 3 1.968 0.0587 0.359
HMC_vs_Metro 4 0.983 0.334 0.179
HMC_vs_SMC 0 -0.621 0.539 -0.113
HMC_vs_SMC 1 6.379 5.67e-07 1.165
HMC_vs_SMC 2 6.148 1.06e-06 1.122
HMC_vs_SMC 3 33.389 1.07e-24 6.096
HMC_vs_SMC 4 282.803 1.89e-51 51.632
DEMetro_Z_vs_SMC 0 2.785 0.00934 0.508
DEMetro_Z_vs_SMC 1 5.239 1.31e-05 0.956
DEMetro_Z_vs_SMC 2 4.772 4.77e-05 0.871
DEMetro_Z_vs_SMC 3 12.041 8.35e-13 2.198
DEMetro_Z_vs_SMC 4 13.200 8.64e-14 2.410
Mean Rmse (scatter)
Glass’s Δ Mean RMSE
Glass Δ Mean RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.732 0.101 0.073 8.655
HMC 3.0 1.321 0.129 0.094 12.725
HMC 4.0 1.751 0.097 0.069 23.935
HMC 10.0 5.474 0.088 0.080 67.200
HMC 50.0 5.655 0.087 0.060 93.216
SMC 2.1 0.837 0.101 0.073 10.083
SMC 3.0 0.245 0.129 0.094 1.244
SMC 4.0 0.128 0.097 0.069 0.449
SMC 10.0 0.088 0.088 0.080 0.006
SMC 50.0 0.107 0.087 0.060 0.325
Metro 2.1 0.339 0.101 0.073 3.260
Metro 3.0 0.588 0.129 0.094 4.899
Metro 4.0 1.897 0.097 0.069 26.049
Metro 10.0 4.694 0.088 0.080 57.467
Metro 50.0 5.529 0.087 0.060 91.118
DEMetro_Z 2.1 1.846 0.101 0.073 23.919
DEMetro_Z 3.0 1.320 0.129 0.094 12.711
DEMetro_Z 4.0 2.054 0.097 0.069 28.312
DEMetro_Z 10.0 4.653 0.088 0.080 56.954
DEMetro_Z 50.0 4.803 0.087 0.060 78.965
Var Rmse
var_rmse plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 -1.083 0.287 -0.203
HMC 3.0 2.669 0.0104 0.950
HMC 4.0 3.888 0.000541 32.777
HMC 10.0 28.164 1.26e-22 261.622
HMC 50.0 1094.111 7.94e-127 281.285
SMC 2.1 -1.269 0.215 -0.233
SMC 3.0 -1.332 0.192 -0.248
SMC 4.0 -1.521 0.134 -0.391
SMC 10.0 0.247 0.805 0.065
SMC 50.0 -0.518 0.606 -0.122
Metro 2.1 -1.063 0.296 -0.201
Metro 3.0 0.492 0.625 0.110
Metro 4.0 3.723 0.000845 56.002
Metro 10.0 11.343 3.5e-12 219.119
Metro 50.0 32.687 1.89e-24 272.878
DEMetro_Z 2.1 0.059 0.953 0.012
DEMetro_Z 3.0 3.016 0.00438 1.307
DEMetro_Z 4.0 3.744 0.000797 59.431
DEMetro_Z 10.0 11.113 5.71e-12 220.637
DEMetro_Z 50.0 12.440 3.75e-13 235.729
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
HMC_vs_SMC 0 0.799 0.431 0.146
HMC_vs_SMC 1 3.772 0.00074 0.689
HMC_vs_SMC 2 3.947 0.000462 0.721
HMC_vs_SMC 3 28.156 1.3e-22 5.141
HMC_vs_SMC 4 1222.400 6.96e-70 223.179
Metro_vs_DEMetro_Z 0 -2.071 0.0474 -0.378
Metro_vs_DEMetro_Z 1 -2.966 0.00599 -0.541
Metro_vs_DEMetro_Z 2 -0.178 0.86 -0.033
Metro_vs_DEMetro_Z 3 -0.072 0.943 -0.013
Metro_vs_DEMetro_Z 4 1.742 0.0921 0.318
HMC_vs_Metro 0 -0.045 0.965 -0.008
HMC_vs_Metro 1 2.342 0.0262 0.428
HMC_vs_Metro 2 -1.296 0.205 -0.237
HMC_vs_Metro 3 1.891 0.0686 0.345
HMC_vs_Metro 4 1.005 0.323 0.184
HMC_vs_DEMetro_Z 0 -2.251 0.0321 -0.411
HMC_vs_DEMetro_Z 1 -0.690 0.496 -0.126
HMC_vs_DEMetro_Z 2 -1.535 0.136 -0.280
HMC_vs_DEMetro_Z 3 1.787 0.0843 0.326
HMC_vs_DEMetro_Z 4 2.404 0.0228 0.439
Metro_vs_SMC 0 0.661 0.514 0.121
Metro_vs_SMC 1 2.644 0.0131 0.483
Metro_vs_SMC 2 3.748 0.00079 0.684
Metro_vs_SMC 3 11.355 3.42e-12 2.073
Metro_vs_SMC 4 32.633 2.05e-24 5.958
DEMetro_Z_vs_SMC 0 2.755 0.01 0.503
DEMetro_Z_vs_SMC 1 3.958 0.000448 0.723
DEMetro_Z_vs_SMC 2 3.766 0.000753 0.688
DEMetro_Z_vs_SMC 3 11.135 5.46e-12 2.033
DEMetro_Z_vs_SMC 4 12.384 4.2e-13 2.261
Var Rmse (scatter)
Glass’s Δ Variance RMSE
Glass Δ Variance RMSE
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 6.256 13.069 33.570 -0.203
HMC 3.0 3.798 1.344 2.582 0.950
HMC 4.0 7.273 0.388 0.210 32.777
HMC 10.0 43.231 0.212 0.164 261.622
HMC 50.0 45.206 0.226 0.160 281.285
SMC 2.1 5.258 13.069 33.570 -0.233
SMC 3.0 0.705 1.344 2.582 -0.248
SMC 4.0 0.306 0.388 0.210 -0.391
SMC 10.0 0.223 0.212 0.164 0.065
SMC 50.0 0.207 0.226 0.160 -0.122
Metro 2.1 6.326 13.069 33.570 -0.201
Metro 3.0 1.627 1.344 2.582 0.110
Metro 4.0 12.152 0.388 0.210 56.002
Metro 10.0 36.242 0.212 0.164 219.119
Metro 50.0 43.861 0.226 0.160 272.878
DEMetro_Z 2.1 13.467 13.069 33.570 0.012
DEMetro_Z 3.0 4.719 1.344 2.582 1.307
DEMetro_Z 4.0 12.872 0.388 0.210 59.431
DEMetro_Z 10.0 36.492 0.212 0.164 220.637
DEMetro_Z 50.0 37.921 0.226 0.160 235.729
Wasserstein Distance
wasserstein_distance plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 6.166 8.48e-07 7.728
HMC 3.0 7.511 2.52e-08 15.127
HMC 4.0 6.396 5.31e-07 26.106
HMC 10.0 31.142 4.67e-24 70.156
HMC 50.0 69.595 1.27e-34 103.704
SMC 2.1 7.944 6.86e-09 10.083
SMC 3.0 3.417 0.00154 1.749
SMC 4.0 1.819 0.0741 0.469
SMC 10.0 0.224 0.824 0.053
SMC 50.0 0.695 0.49 0.183
Metro 2.1 5.177 1.07e-05 3.593
Metro 3.0 4.721 5.07e-05 6.167
Metro 4.0 4.534 9.22e-05 28.602
Metro 10.0 12.874 1.54e-13 61.779
Metro 50.0 36.639 5.17e-26 97.467
DEMetro_Z 2.1 5.159 1.61e-05 20.834
DEMetro_Z 3.0 6.026 1.43e-06 15.524
DEMetro_Z 4.0 4.911 3.24e-05 32.043
DEMetro_Z 10.0 11.800 1.32e-12 61.373
DEMetro_Z 50.0 13.266 7.43e-14 85.583
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
Metro_vs_DEMetro_Z 0 -4.237 0.000209 -0.774
Metro_vs_DEMetro_Z 1 -3.102 0.00426 -0.566
Metro_vs_DEMetro_Z 2 -0.423 0.675 -0.077
Metro_vs_DEMetro_Z 3 0.073 0.942 0.013
Metro_vs_DEMetro_Z 4 1.664 0.107 0.304
DEMetro_Z_vs_SMC 0 2.512 0.0178 0.459
DEMetro_Z_vs_SMC 1 5.377 8.91e-06 0.982
DEMetro_Z_vs_SMC 2 4.819 4.19e-05 0.880
DEMetro_Z_vs_SMC 3 11.874 1.17e-12 2.168
DEMetro_Z_vs_SMC 4 13.176 9.04e-14 2.406
HMC_vs_DEMetro_Z 0 -3.014 0.00531 -0.550
HMC_vs_DEMetro_Z 1 -0.118 0.907 -0.022
HMC_vs_DEMetro_Z 2 -0.826 0.415 -0.151
HMC_vs_DEMetro_Z 3 1.527 0.138 0.279
HMC_vs_DEMetro_Z 4 2.530 0.0171 0.462
HMC_vs_Metro 0 2.792 0.00918 0.510
HMC_vs_Metro 1 3.356 0.00222 0.613
HMC_vs_Metro 2 -0.326 0.747 -0.060
HMC_vs_Metro 3 1.578 0.125 0.288
HMC_vs_Metro 4 2.286 0.0297 0.417
HMC_vs_SMC 0 -1.252 0.221 -0.229
HMC_vs_SMC 1 6.495 4.14e-07 1.186
HMC_vs_SMC 2 6.191 9.43e-07 1.130
HMC_vs_SMC 3 30.431 1.47e-23 5.556
HMC_vs_SMC 4 69.692 7.64e-34 12.724
Metro_vs_SMC 0 -4.881 3.53e-05 -0.891
Metro_vs_SMC 1 2.875 0.00748 0.525
Metro_vs_SMC 2 4.499 0.000102 0.821
Metro_vs_SMC 3 12.992 1.29e-13 2.372
Metro_vs_SMC 4 36.595 7.98e-26 6.681
Wasserstein Distance (scatter)
Glass’s Δ WS
Glass Δ WS
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.758 0.179 0.075 7.728
HMC 3.0 1.203 0.156 0.069 15.127
HMC 4.0 1.590 0.118 0.056 26.106
HMC 10.0 4.784 0.101 0.067 70.156
HMC 50.0 5.245 0.099 0.050 103.704
SMC 2.1 0.935 0.179 0.075 10.083
SMC 3.0 0.277 0.156 0.069 1.749
SMC 4.0 0.144 0.118 0.056 0.469
SMC 10.0 0.105 0.101 0.067 0.053
SMC 50.0 0.108 0.099 0.050 0.183
Metro 2.1 0.449 0.179 0.075 3.593
Metro 3.0 0.583 0.156 0.069 6.167
Metro 4.0 1.731 0.118 0.056 28.602
Metro 10.0 4.225 0.101 0.067 61.779
Metro 50.0 4.936 0.099 0.050 97.467
DEMetro_Z 2.1 1.740 0.179 0.075 20.834
DEMetro_Z 3.0 1.231 0.156 0.069 15.524
DEMetro_Z 4.0 1.925 0.118 0.056 32.043
DEMetro_Z 10.0 4.198 0.101 0.067 61.373
DEMetro_Z 50.0 4.346 0.099 0.050 85.583
Mmd Rff
mmd_rff plot
Sampler vs IID stats
Sampler Varying t-stat p-value Glass Δ
HMC 2.1 5.931 1.78e-06 10.720
HMC 3.0 6.885 1.35e-07 15.493
HMC 4.0 6.358 5.9e-07 26.602
HMC 10.0 34.839 1.63e-25 69.905
HMC 50.0 159.706 1.52e-50 102.650
SMC 2.1 7.128 6.79e-08 12.932
SMC 3.0 3.045 0.00415 1.427
SMC 4.0 1.548 0.127 0.402
SMC 10.0 0.293 0.771 0.066
SMC 50.0 0.929 0.357 0.251
Metro 2.1 4.808 3.31e-05 3.586
Metro 3.0 4.347 0.000145 5.830
Metro 4.0 4.490 0.000104 28.047
Metro 10.0 13.211 8.04e-14 59.761
Metro 50.0 43.784 2.65e-28 100.754
DEMetro_Z 2.1 4.882 3.51e-05 31.682
DEMetro_Z 3.0 5.676 3.77e-06 15.528
DEMetro_Z 4.0 4.920 3.16e-05 31.212
DEMetro_Z 10.0 12.068 7.6e-13 59.925
DEMetro_Z 50.0 13.523 4.59e-14 86.835
Sampler vs Sampler stats
Sampler Pair Varying t-stat p-value Cohen’s d
DEMetro_Z_vs_SMC 0 2.756 0.01 0.503
DEMetro_Z_vs_SMC 1 5.155 1.65e-05 0.941
DEMetro_Z_vs_SMC 2 4.838 3.98e-05 0.883
DEMetro_Z_vs_SMC 3 12.142 6.8e-13 2.217
DEMetro_Z_vs_SMC 4 13.432 5.59e-14 2.452
HMC_vs_Metro 0 3.567 0.00128 0.651
HMC_vs_Metro 1 3.336 0.00234 0.609
HMC_vs_Metro 2 -0.190 0.851 -0.035
HMC_vs_Metro 3 1.977 0.0576 0.361
HMC_vs_Metro 4 0.763 0.452 0.139
Metro_vs_DEMetro_Z 0 -4.410 0.00013 -0.805
Metro_vs_DEMetro_Z 1 -3.057 0.00477 -0.558
Metro_vs_DEMetro_Z 2 -0.392 0.698 -0.072
Metro_vs_DEMetro_Z 3 -0.032 0.975 -0.006
Metro_vs_DEMetro_Z 4 2.008 0.054 0.367
HMC_vs_SMC 0 -0.786 0.438 -0.144
HMC_vs_SMC 1 6.166 1.01e-06 1.126
HMC_vs_SMC 2 6.172 9.94e-07 1.127
HMC_vs_SMC 3 33.907 6.94e-25 6.190
HMC_vs_SMC 4 158.375 3.75e-44 28.915
Metro_vs_SMC 0 -5.024 2.37e-05 -0.917
Metro_vs_SMC 1 2.851 0.00794 0.521
Metro_vs_SMC 2 4.458 0.000114 0.814
Metro_vs_SMC 3 13.351 6.5e-14 2.438
Metro_vs_SMC 4 44.028 4.1e-28 8.038
HMC_vs_DEMetro_Z 0 -3.040 0.00498 -0.555
HMC_vs_DEMetro_Z 1 -0.010 0.992 -0.002
HMC_vs_DEMetro_Z 2 -0.666 0.511 -0.122
HMC_vs_DEMetro_Z 3 1.787 0.0844 0.326
HMC_vs_DEMetro_Z 4 2.454 0.0204 0.448
Mmd Rff (scatter)
Glass’s Δ MMD-RFF
Glass Δ MMD-RFF
Glass’s Δ table
Sampler Varying MCMC Mean IID Mean IID Std Glass’s Δ
HMC 2.1 0.074 0.010 0.006 10.720
HMC 3.0 0.148 0.014 0.009 15.493
HMC 4.0 0.199 0.011 0.007 26.602
HMC 10.0 0.601 0.010 0.008 69.905
HMC 50.0 0.619 0.009 0.006 102.650
SMC 2.1 0.087 0.010 0.006 12.932
SMC 3.0 0.026 0.014 0.009 1.427
SMC 4.0 0.014 0.011 0.007 0.402
SMC 10.0 0.010 0.010 0.008 0.066
SMC 50.0 0.011 0.009 0.006 0.251
Metro 2.1 0.031 0.010 0.006 3.586
Metro 3.0 0.064 0.014 0.009 5.830
Metro 4.0 0.209 0.011 0.007 28.047
Metro 10.0 0.515 0.010 0.008 59.761
Metro 50.0 0.608 0.009 0.006 100.754
DEMetro_Z 2.1 0.198 0.010 0.006 31.682
DEMetro_Z 3.0 0.148 0.014 0.009 15.528
DEMetro_Z 4.0 0.232 0.011 0.007 31.212
DEMetro_Z 10.0 0.517 0.010 0.008 59.925
DEMetro_Z 50.0 0.525 0.009 0.006 86.835
Runtime
runtime plot
Runtime (scatter)
Ess
ess plot
Ess (scatter)
Ess Per Sec
ess_per_sec plot
Ess Per Sec (scatter)
R Hat
r_hat plot
Mode Transitions
mode_transitions plot
Mode Transitions (scatter)
KDE + Init Plots
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
KDE plot Pooled Init Plot Chain Init Plot
Trace Plots
Pooled
2.1 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
3 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
4 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
10 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
50 HMC pooled trace Metro pooled trace SMC pooled trace DEMetro_Z pooled trace
Chain
2.1 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
3 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
4 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
10 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
50 HMC chain trace Metro chain trace SMC chain trace DEMetro_Z chain trace
Pairwise Scatter Plots
Pooled
2.1
3
4
10
50
Chain
2.1
3
4
10
50